One English word that describes someone who does not admit their wrongdoings is unrepentant. The Oxford English Dictionary defines the word thus:
Feeling or evincing no regret for one’s wrongdoings; impenitent. Now also more generally: not sorry for any action or behaviour, unapologetic.
The word is not restricted to referring to one's attitude at death. That said, the word is sometimes used to refer to people who do not repent from their wrongdoing before death or the Last Judgment, especially in a Christian context. The OED has several examples of unrepentant used in the face of death:
Bible (Wycliffite, E.V.) (Douce 369(2)) (1850) Rom. ii. 5 Aftir thi hardnesse and vnrepentaunt [L. impaenitens] herte, thou tresourist to thee wraththe in to the day of wraththe. [Translation: Befitting your hardness and unrepentant heart, you store up wrath to yourself for the day of wrath.]
c1450 Jacob's Well (1900) 9 In þis cursyng, who-so deye vnrepentaunt, schal haue a dredeful ende! [Translation: In this cursing, whoever dies unrepentant shall have a dreadful end!]
1796 W. Cole Contradiction 144 May I die unrepentant and unforgiven, if my humiliation come not from my heart; if my contrition be not sincere!
Today, it is very common to see unrepentant describing someone who is very obviously bad: two of the top collocations for unrepentant with a noun are unrepentant sinner and unrepentant terrorist. Otherwise, unrepentant is frequently used as a predicate adjective describing the subject of the sentence, as the first results from a COCA search show (Corpus of Contemporary American English):
The prodigal is allowed to return even if unrepentant.
Buchanan as ever was unrepentant about his and his wife's aim.
Ledstone was quite unrepentant about his grandfather.