Suppose an ignorant person dies in a car accident. Has ignorance come to an end for that person?
We don't know. The Buddha would in each case know if a person possible got rid of ignorance by death, would know the destiny of certain being.
Nope. Karma and rebirth are essential parts of Buddhism - one could have a long debate on it.
To put it (deceptively) simply: if nothing else does, ignorance surely does survive.
This question appears to believe there is a lasting "person" or "self". It is not Buddhist but, instead, 'Eternalism', as follows:
And how, bhikkhus, do some hold back? Devas and humans enjoy being, delight in being, are satisfied with being. When Dhamma is taught to them for the cessation of being, their minds do not enter into it or acquire confidence in it or settle upon it or become resolved upon it. Thus, bhikkhus, do some hold back. Iti 49
In Buddhism, this question is considered the question of the Evil One Mara (Satan), as follows:
Then Mara the Evil One, desiring to arouse fear, trepidation, and terror in the bhikkhuni Vajira, desiring to make her fall away from concentration, approached her and addressed her in verse:
By whom has this being been created? Where is the maker of the being? Where has the being arisen? Where does the being cease?
MN 2 says this question is inappropriate increasing suffering, as follows:
Through his attending to ideas unfit for attention and through his not attending to ideas fit for attention, both unarisen fermentations arise in him, and arisen fermentations increase.
This is how he attends inappropriately: 'Was I in the past? Was I not in the past? What was I in the past? How was I in the past? Having been what, what was I in the past? Shall I be in the future? Shall I not be in the future? What shall I be in the future? How shall I be in the future? Having been what, what shall I be in the future?' Or else he is inwardly perplexed about the immediate present: 'Am I? Am I not? What am I? How am I? Where has this being come from? Where is it bound?'
As he attends inappropriately in this way, one of six kinds of view arises in him: The view I have a self arises in him as true & established, or the view I have no self... or the view It is precisely by means of self that I perceive self... or the view It is precisely by means of self that I perceive not-self... or the view It is precisely by means of not-self that I perceive self arises in him as true & established, or else he has a view like this: This very self of mine — the knower that is sensitive here & there to the ripening of good & bad actions — is the self of mine that is constant, everlasting, eternal, not subject to change, and will stay just as it is for eternity. This is called a thicket of views, a wilderness of views, a contortion of views, a writhing of views, a fetter of views. Bound by a fetter of views, the uninstructed run-of-the-mill person is not freed from birth, aging, & death, from sorrow, lamentation, pain, distress, & despair. He is not freed, I tell you, from suffering & stress.
In Buddhism, "the person" ("puggalo") is merely a "name" (nāmo) that attaches itself conventionally to five aggregates. The Buddhist view is it is five aggregates that end in a fatal car accident rather than "a person".
"Death" ("marana") occurs not to those perished five aggregates but to the surviving loved ones (the "clan"; "gotto") of those perished five aggregates deceased in the accident because the survivors grieve over their loss to the idea of "a being" or "self" or "person" their minds have manufactured though ignorance.
At Savatthi…. There the Blessed One said this:
Bhikkhus, I will teach you the burden, the carrier of the burden, the taking up of the burden, and the laying down of the burden. Listen to that….
And what, bhikkhus, is the burden? It should be said: the five aggregates subject to clinging. What five? The form aggregate subject to clinging, the feeling aggregate subject to clinging, the perception aggregate subject to clinging, the volitional formations aggregate subject to clinging, the consciousness aggregate subject to clinging. This is called the burden.
And what, bhikkhus, is the carrier of the burden? It should be said: the person (puggalo), this venerable one of such a name (nāmo) and clan (gotto). This is called the carrier of the burden.
And what, bhikkhus, is the taking up of the burden? It is this craving that leads to renewed existence, accompanied by delight and lust, seeking delight here and there; that is, craving for sensual pleasures, craving the be, craving not to be. This is called the taking up of the burden.
And what, bhikkhus, is the laying down of the burden? It is the remainderless fading away and cessation of that same craving, the giving up and relinquishing of it, freedom from it, non-reliance on it. This is called the laying down of the burden.