Non-sentient beings and sentient beings

There is a class of "insentient" being in the Buddhadharma called the asaṃjñasattva, a class of devas in the bṛhatphalā heaven of the fourth dhyāna. This is maybe what you mean? These live lives of non-perception until perception arises when they are reborn in a lower state after their merit has exhausted itself and their lifespan ends.

From Abhidhamma in Daily Life by Venerable Janakabhivamsa (Chanmyay Sayadaw):

Asannasatta Brahmas: Asannasatta Brahmas are those divine beings without any consciousness or mind. As human beings they discover the faults of citta (mind) and sañña (memory). They see that all forms of greed arises because of citta, they also see that life would be so peaceful had there been no citta. While concentrating on the fault of consciousness, “Citta is loathsome. Citta is loathsome”, they develop a kammatthana called sannaviraga bhávaná - disgust for sañña.

When they die they are reborn as Brahmas, in the Asannasatta Brahma realms and live like golden statues, standing, sitting or reclining without consciousness. Their life span is 500 kappa’s long.

That was a Theravādin Venerable expounding. This is from Abhidharmakośakārikā as translated by Louis de La Vallée-Poussin:

What is non-consciousness (āsaṃjñika)?

Non-consciousness is that which, among the Nonconscious Ones, arrests the mind and its mental states. Among the beings who take birth among the Non-Conscious Ones, i.e., the non-conscious gods, there is a dharma that arrests the mind and its mental states, and which is called "non-consciousness." By this dharma, the mind and future dharmas are, for a certain time, hindered from being produced and do not have the power to arise. This dharma is similar to what arrests the water of a river, that is, (similar) to a dike.

This dharma is exclusively retribution. It is exclusively the retribution of non-conscious absorption (asaṃjñāsamāpatti, ii.42a).

Where do these non-conscious gods reside?

They live in bṛhatphalā. In the heaven of the bṛhatphalās there is a raised place which is the dwelling of the Non-Conscious Ones, in the same way as the dhyānāntarikā, the dwelling of the Mahābrahmā gods, is raised withinnthe heaven of the Brahmapurohitas (iii.2c;222 Vibhāsa, TD 27, p.784b5).

Are the Non-Conscious Ones called this because they are always non-conscious, or are they sometimes conscious?

They are conscious at birth and at death (iii.42; Vibhāsa, TD 27, p. 784c8); they are called non-conscious because their consciousness is suspended for a very long time. When, after this long time, they produce a consciousness again, they die. As it says in the Sutra "When they produce consciousness again, they die, like a person awakening after sleep." Dying in the non-conscious heaven, they are necessarily reborn in the Kāmadhātu and nowhere else. (1) In fact, the force of asaṃjñāsamāpatti (ii.42a), by which these beings are born among the Non-Conscious Ones, is exhausted; they have not been in a position to practice asaṃjñāsamāpatti: hence they die, as arrows fall to the ground when their impetus is spent. (2) On the other hand, beings who are reborn among the Non-Conscious Ones necessarily possess an action "retributive in kāmadhātu" and "retributive in the second existence" (iv.50b).

Devas of even higher classes could be described as "non-sentient" to various degrees but even those without perception, with neither perception nor non-perception etc., eventually die.

In the original Pali Buddhism, "a being" ("satta") means "clinging" and is a wrong view (refer to SN 23.2 & SN 5.10). Therefore it is not possible for any "being" to reach Nirvana; since all "beings" abide in samsara; hindered by ignorance and fettered by craving, assuming form, feeling, perception, formations &/or consciousness to be a self (per SN 22.99).

It appears the emphasis about "sentient beings" is in Mahayana.

Idk what u mean by Non sentient beings but maybe one can say that of plants as in they are according to Sutta 'alive but aren't percepient'.