Can a Sovereign-will authorize personal liberty?

You are correct that sovereignty relates to authority. Where God is concerned, he is at the top.

There are however Christians who will profess that God is "In Control" of everything that happens. For example, if someone gets cancer, they will make the remark that whatever happens that "God is in control". I've also had friends die from cancer and their partners would say it must have been "God's will" for them to die.

Caseyr547 is right to say that this type of thinking stems from Calvanism. This "hyper sovereignty" as I'd call it is a particularly prevalent doctrine in the Open Brethren churches. The NIV bible even translated phrases like "God Almighty" for "Sovereign Lord" in just about every place in the NIV text popularising the term.

People who take this view on the sovereignty of God also use scripture to back their view such as Romans 8:28.- all things work together for good...

I hope this answers it for you.

I would go on to say that in my experience this Sovereignty of God doctrine is a convenient doctrine and gives some comfort to people as it means they don't have to do anything. It calls for believers to be passive.

However, scripture makes it perfectly clear that God does not override our decisions. For example, God did not override Adam and Eve's decision to eat the forbidden fruit. God guided Cain to make a right choice, but Cain still chose to go his own way. Many of the things that happen in life as a result of the original sin. We still live in a cursed world.

Just like an earthly king has to enforce his will through people, God uses people and in particular his church to bring about change in the world and to preach the gospel. If his church are not preaching the gospel then people will not be saved. It's still his will that people be saved regardless of what his church does.

Technically, Reformed Theology does not exclude liberty from sovereignty. Quoting from The Westminster Confession of Faith, Chapter III, point I:

I. God from all eternity, did, by the most wise and holy counsel of His own will, freely, and unchangeably ordain whatsoever comes to pass; yet so, as thereby neither is God the author of sin, nor is violence offered to the will of the creatures; nor is the liberty or contingency of second causes taken away, but rather established.

Calvinists define free will as the freedom to act according to one's nature. From a Reformed perspective, including a truly random perturbation to provide a certain kind of freedom would not increase the power of the individual's will — the perturbation would be just as external as a Divine decree — but rather establish a lesser but coworking god called Chance to which (in some small part) creation would be subject.

Similarly, God accidentally getting creation just a little wrong so that unintended consequences occur would not increase the freedom of the individual, but such would indicate an imperfection in God. Such a concept of a fallible God is offensive to many Christians.

In his letter to the Romans, Paul provides a response to one complaint about such sovereignty. (This response seems similar to what God told Job — effectively, 'I am God and you are not'.)

One of you will say to me: "Then why does God still blame us? For who resists his will?" But who are you, O man, to talk back to God? "Shall what is formed say to him who formed it, 'Why did you make me like this?'" Does not the potter have the right to make out of the same lump of clay some pottery for noble purposes and some for common use? (Romans 8:19-21 [NIV])

The writers of The Westminster Confession of faith closed Chapter III with a recognition that such is a difficult teaching and with a declaration that this teaching is not an encouragement to passivity but rather toward worship and obedience (and peace/assurance):

VIII. The doctrine of this high mystery of predestination is to be handled with special prudence and care, that men, attending the will of God revealed in His Word, and yielding obedience thereunto, may, from the certainty of their effectual vocation, be assured of their eternal election. So shall this doctrine afford matter of praise, reverence, and admiration of God; and of humility, diligence, and abundant consolation to all that sincerely obey the Gospel.