Could someone who had joined a monastery decide to leave?

This depends on the reason why the person was living in a monastery. Often monasteries were used as prisons explicitly. Some people were simply forbidden leaving, this often happened with people who were criminals, rebels or lost power struggle with opponents but for some reasons their lives were spared. In other words, monasteries often were used as a humane "execution" of a person, the same way as the mental institutions are used in modern Russia.

But the majority could leave. They definitely better would obtain a kind of blessing for that from their superiors though, but generally it was not necessary.

Some influential people sometimes went to live in a monastery, only to make comeback later (Ivan the Terrible, for instance).

"Decide to leave" was always an option to consider.

And one could do that, of course. Just do that. But it seems the question is more about the obstacles and costs that may be associated with that?

As, obviously, also when in prison anyone might decide to leave. Can't she?

It is an incredibly large timeframe to analyze and no clear geographical boundary and no clear distinction for what faith or even order this should be analyzed against.

Usually, monks and nuns were expected to keep their vows and remain. That would be on different levels of difficulty for those joining at a young or relatively older age. Whether it was voluntary or by some form of pressure. Especially for those joining at a very young age "return to the life they lived before joining" would be impossible? But societal conventions are a matter of constant negotiations and outcomes are not guaranteed. There are many exceptions to the rules.

The most obvious example to look at seems to be Martin Luther.

There were basically three options:

• ask for permission
• run away
• get expelled (not always voluntarily, but possible)

Luther for example wrote a letter simply asking for permission to do so.

So he determined to follow the example of his brethren. The Elector was much surprised one morning by receiving the keys of the convent from Luther, accompanied by a letter, in which he expressed his wish to leave the monastery — lay aside the dress and name of a monk, and be called Doctor Luther. In reply, the Elector sent him a piece of black cloth, told him he might have it made up any way he liked, but that he must not leave the monastery.

— Elizabeth Jane Whately: The story of Martin Luther, 1862. (gBooks)

After his decision and appeal was declined, we know he didn't remain a monk. And we know his future wife was a nun as well. What happened?

Duke George’s opposition to Luther’s attack on monasticism was informed by his pronounced sense of justice. He understood the vows of monks and nuns to be legally binding oaths with far-reaching consequences, such as the loss of all secular legal rights. Dispensation could only be granted by the pope. By leaving their monasteries, Luther’s followers were breaking both ecclesiastical and secular law. It is not surprising that those leaving monasteries were accused of criminal intent. George exploited this theme, claiming that runaway monks and nuns always revealed themselves to be who*es and scoundrels. The duke considered those who broke their vows to be dishonorable, and he consistently refused to acknowledge their legal rights. This was so in the case of a succession in Pirna10 as well as in the attestation of a former prior from the Kőnigstein monastery. George held the witness’s testimony to be worthless because it was known “how much to trust or believe the handwritten testimony of a man who has violated his vow and abandoned his habit and order.” This legal approach to religious vows was particularly evident in his conflict with Luther. By the start of 1523, George had added “apostate runaway monk” to his list of accusations against Luther.

— Christoph Volkmar: "Catholic Reform in the Age of Luther. Duke George of Saxony and the Church, 1488-1525", Studies in Medieval and Reformation Traditions, Volume: 209, Brill: Leiden, Boston, 2017.

After this period, the whole frame of ecclesiastical laws to apply as well as the connecting binds between profane and clerical spheres changes quite much. (Cf. — Anne Jacobson Schutte: "By Force and Fear: Taking and Breaking Monastic Vows in Early Modern Europe", Cornell University Press, 2011.)

One conspicuous example from earlier Catholic Europe, illustrates most of the obstacles and outcomes to expect:

Reading Hrabanus’ strong response to Gottschalk’s demands to leave, […]

As has been argued by earlier scholars, the Liber seems to have been Hrabanus’ riposte to the synod’s decision to award Gottschalk his freedom, since, though it does not mention Gottschalk by name, it concerns a particular monk who wanted to leave the monastery and who was supported by Saxon “notables” (primates). […]

Few options existed for early ninth-century monks wanting to leave the monastic life after taking their vows. There were anonymous runaway oblates and monks, who fled their cloisters without leave, but little is known about what they did thereafter.
Fulda itself had its fair share of runaways in the early ninth century. Such cases are important to this investigation because they show how Gottschalk sought to obtain his freedom through the proper episcopal channels in order to avoid jeopardizing his chances for a career outside Fulda.

Hrabanus also wrote that to disparage a part (species) was to mock the whole (genus). New Testament authors helped him shape his argument, including: (Mt 5, 19) “He who leaves out one of the least of these mandates, and teaches men so, will be called the least in the kingdom of heaven,” which comes from the Sermon on the Mount; (Jac 2, 10) “He who offends in one thing, is made answerable for all”; and other similar quotations. Hrabanus claimed that to blaspheme child oblation led to excommunication and Hell, and the only way to save oneself was through penitence worthy of one’s error. He condemned Gottschalk’s “doctrines” as new and wicked, arguing that instead of the backing of biblical and patristic authorities they were influenced by deceiving spirits of error with demonic teachings.

Whether Gottschalk won Ebbo’s favor again or not with his letter, like all the lesser traitors of 830, his sentence would have been commuted in 831. At that time Louis ordered the release of those forcibly cloistered, allowing them to recover their lost properties and to leave the monastery if they desired.

— Matthew Bryan Gillis: "Heresy and Dissent in the Carolingian Empire The Case of Gottschalk of Orbais", Oxford University Press: Oxford, New York, 2017.

That such conditions didn't apply equally across time and location and organizations is evident when we look at other examples. Like Symeon?

First, he wanted to join:

The father of Symeon the Theologian, as we have seen, was extremely distressed about Symeon's plan to take monastic vows […]
Even after Symeon had entered the Stuodios monastery, his family tried to persuade him to leave. In this case, not only did his father want the son as a support in his declining years, but the family hoped that he would have a successful secular career in Constantinople.

— Alice-Mary Talbot: "The Byzantine Family and the Monastery", Dumbarton Oaks Papers, 1990, Vol. 44 (1990), pp. 119-129.

Clearly showing that life wasn't always turning bad for those leaving a Christian monastery even if the rest of society didn't change confession and power bases.
However, this very person did leave indeed, but not really due to his own volition:

In 1009 Symeon was sent into exile near Paloukiton, a small village near Chrysopolis on the Asiatic shore of the Bosphorus. According to one account, he was left by church authorities alone and without food, in the middle of winter.

Another Monk called Simeon went directly from being Monk to King of the Bulgars, not be heresy but by simple heritage appointment, again demonstrating that any societal conventions are a matter of constant negotiations:

Around 888, Simeon returned to Bulgaria and settled at the newly established royal monastery of Preslav […] Meanwhile, Vladimir had succeeded Boris, who had retreated to a monastery, as ruler of Bulgaria. Vladimir attempted to reintroduce paganism in the empire and possibly signed an anti-Byzantine pact with Arnulf of Carinthia, forcing Boris to re-enter political life. Boris had Vladimir imprisoned and blinded, and then appointed Simeon as the new ruler.

In principle, they were not supposed to leave their order because they took a vow for life. In practice, some did leave, and some were subsequently readmitted. However, the time period covered here is very long, and different orders - and individuals within orders - were probably sometimes more, sometimes less inclined to allow people to leave. Consequently, some just ran away. In short, it's a little complicated.

For Franciscans,

When the year of probation is over, let them be received into obedience, promising to observe this life and rule always; and, according to the command of the lord pope, it will be absolutely forbidden to them to leave the order,...

Novices, though, could leave. This next source on Augustinians also makes this clear:

At the end of the probationary period, the novice was brought to the chapter and asked whether he wished to leave and go his own way or offer himself to God and the order.

Source: Frances Andrews, 'The Other Friars: The Carmelite, Augustinian, Sack and Pied Friars in the Middle Ages'

For Carmelites, the same 'rule' applied:

Once professed, a brother remained subject to the order for life.

Source: Andrews

...and for Benedictines, whose vows included the vow of stability which

binds the monk in both body and spirit to the community of his profession for the rest of his life, where he serves under both a Rule and an Abbot.

Thus Benedictines, unlike Franciscans for example, weren't just bound to the order but to a specific monastery.

However, despite these vows, there were occasions when monks and nuns were either allowed to leave, forced to leave or ran away. The writer (or writers) of the 6th century Regula Magistri (Rule of the Master) were not so naïve as to believe that some recruits would not want to leave:

...in the Rule we read that the new member’s old clothes are to be “placed in the vestiary to be preserved; so that if, at any time, the devil persuading him, he shall consent to go forth from the monastery — may it not happen — then, taking off the garments of the monastery, he may be cast out”

Source: Sherri Olson, 'Daily Life in a Medieval Monastery' (2013)

Being readmitted was possible, even after leaving more than once. On "Whether brothers who leave the monastery ought again to be received",

A brother who goes out, or is cast out, of the monastery for his own fault, if he wishes to return, shall first promise every amends for the fault.… But if he again departs, up to the third time he shall be received. Knowing that after this every opportunity of return is denied to him.

Cited in Olson

One such case was recorded at Ouville in Normandy:

In 1249 at Ouville, a house of Augustinian canons, Eudes orders the prior to prepare a separate place in the house for John Gaul, who had often withdrawn from the order. He was not to be allowed to be at large in the monastery, no one was to talk to him without permission from the prior, and a book should be given to him “that he may sing his Hours” alone. He is free to leave the house altogether if he wishes, but if he does so he is to be “permanently expelled from the order.”

Source: Olson

And also in 7th century Gaul for nuns,

Waldebert adapts for nuns a chapter of the Benedictine rule in which the author suggests a more relaxed enclosure as it applied to monks. Benedict allows the monk up to three opportunities to return to the community if he “through his own evil action departs from the monastery.” Once readmitted, the monk was expected to make amends for his faults after which he returned to the community in the lowest rank.

Breaking rules was one possible way to be forced to leave, but this could also backfire and lead to imprisonment. For example, among Carmelites in the 13th century,

Inevitably, not all recruits were ready to keep the observance or happy to remain, but any departure from the rule was subject to harsh discipline. Already in 1227 Gregory IX allowed the prior to deal with apostates (runaways) from the order and by 1269 the prior general was authorised to excommunicate and imprison both apostates and the disobedient.

Source: Andrews

Over time, though, it is clear that different standards were applied and that much depended on the Abbot or Abbess. One could simply ask, as in the case of the story of this monk told by Pope Gregory the Great in his biography of St. Benedict:

A monk who “had become unstable in spirit” continually asked Benedict to let him leave the monastery and made such a nuisance of himself that Benedict “angrily ordered him to leave”

Source: Olson

Getting out with the approval of a higher authority clearly wasn't easy sometimes. One nun, Joan of Leeds, resorted to faking her own death. In 1318, the archbishop of York, William Melton, wrote in a letter that Joan,

“with the help of numerous of her accomplices, evildoers, with malice aforethought, crafted a dummy in the likeness of her body in order to mislead the devoted faithful, and she had no shame in procuring its burial in a sacred space amongst the religious of that place.”

Even for royalty, abandoning one's vows could bring about stern sanctions. On the death of Offa, King of Mercia, Eadberht III Præn of Kent led a rebellion in 796 AD against Mercian control, apparently abandoning his vows in the process. Eadberht claimed otherwise but Pope Leo III recognized

Eadberht’s earlier ordination and consequent ineligibility for the kingship....The Church had no alternative but to condemn him, excommunicate and reject him, as Pope Leo put it, ‘having regard to the safety of his soul’

Source: D. P. Kirby, 'The Earliest English Kings' (2001)

One option to life-long vows for men and women from the 13th to the 16th centuries was to be Beguines (women) and Beghards (men) instead. They

...lived in semi-monastic communities but did not take formal religious vows....although they promised not to marry "as long as they lived as Beguines," to quote one of the early Rules, they were free to leave at any time.

Monks and nuns could also be given the choice to leave, or forced, when larger events came to the fore. A classic example is the Dissolution of the Monasteries in England, when the devotion of the vast majority of monks and nuns became evident:

Nunneries were especially vulnerable as the wheels of the Dissolution began to turn, because the smallest and poorest houses were targeted first. In 1536 an act was passed to “suppress” (i.e., take into the king’s hands) the “lesser monasteries,” defined as houses with an annual income under £200.... Given the choice to leave the monastic life or be transferred to another house, most nuns chose the latter: out of a total of roughly 900 women, only 100 chose to renounce their vows in 1536–1537.

Source: Andrews

Eventually, though, most of these larger houses were closed as well so thousands of monks and nuns were forced out.

Also subject to powers beyond their control were the some Sack Friars, who survived by begging. The order of prohibition of some mendicant orders was formalised at the Second Council of Lyon in 1274. Otto, the rector general, wrote to his members to tell them that, as per constitution 23,

...they could now leave the order: those who wished to, should do ‘whatever seemed good in their own eyes’, a direct contradiction of the normal stipulation that regular religious must submit to the will of the superior without hesitation.

Source: Olson