According to the Buddha, ignorance doesn’t have a discoverable beginning, but it still has dependent conditions. In the case of Arahats, it has an end, but it’s possible for a a person to stay unenlightened forever. In that case, it would have neither a beginning nor an end, so is ignorance anicca or nicca?
It’s anicca. You can look at that as either it arises and ceases incessantly, on a more momentary view, or that it is subject to cessation.
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The main practical application of this subject is that in the presence of a state of mind of ignorance, anicca literally causes suffering (dukkha). In the suttas the two (anicca and dukkha) are almost always linked. In that way ignorance is connected to impermanence as fire is connected to fuel.
The opposite is also true:
However, when teaching his own disciples, the Buddha used nibbana more as an image of freedom. Apparently, all Indians at the time saw burning fire as agitated, dependent, and trapped, both clinging and being stuck to its fuel as it burned. To ignite a fire, one had to “seize” it. When fire let go of its fuel, it was “freed,” released from its agitation, dependence, and entrapment — calm and unconfined."—Thanissaro
Has someone already asked somewhere in an old thread here “Is anicca itself also anicca? If so, then will it stops being anicca? Or because it’s always anicca so it’s actually not anicca because its anicca way does not change?”
Sorry to derail the thread, just an old man mumbling, please pardon me and move on. 
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It is presented as hetu paccaya “root condition”, hence the most persistent where anicca is applicable (arising, persisting and fading away). This persistence implies leaving a trace unless uprooted completely, hence Avijjayatveva asesa–viraga–nirodha sankhara–nirodho.
Unchastity is the taint in a woman; niggardliness is the taint in a giver. Taints, indeed, are all evil things, both in this world and the next. A worse taint than these is ignorance, the worst of all taints. Destroy this one taint and become taintless, O monks!
I think ignorance can’t cease, not even for a moment, unless one becomes an Arahat:
Ignorance originates from defilement. Ignorance ceases when defilement ceases. The practice that leads to the cessation of ignorance is simply this noble eightfold path…Defilement originates from ignorance. Defilement ceases when ignorance ceases.
MN 9
This means that ignorance is dependent on previous taint, and the previous taint depends on previous ignorance, and so on. In this way they form a beginningless chain. However, if ignorance ceases for a moment, future taints don’t arise, which makes further ignorance impossible as well. I think that’s why awakening is irreversible.
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yes, I remember that thread as well. I don’t know the reference precisely, but the Buddha said that whether or not there’s the arising of Buddhas, the Dhamma stays the same, which implies it’s nicca, so I think anicca doesn’t apply to abstract concepts (It’s worth it to point out that our views are anicca though). In any case, ignorance seems to be a different case since it isn’t abstract: it’s something that we possess quite literally.
Ah yes, the pitfalls of literalism. 