Я думаю, здесь важен контекст. Не лучший словарь, но в качестве иллюстрации к сказанному пойдёт.
http://context.reverso.net/%D0%BF%D0%B5%D1%80%D0%B5%D0%B2%D0%BE%D0%B4/%D1%80%D1%83%D1%81%D1%81%D0%BA%D0%B8%D0%B9-%D0%B0%D0%BD%D0%B3%D0%BB%D0%B8%D0%B9%D1%81%D0%BA%D0%B8%D0%B9/%D0%9F%D0%BE%D1%81%D0%BB%D0%B5%D0%B4%D0%BD%D0%B8%D0%B5+%D0%B4%D0%BD%D0%B8

THE last days

I just thought it was about the film/movie https://ru.wikipedia.org/wiki/%D0%9F%D0%BE%D1%81%D0%BB%D0%B5%D0%B4%D0%BD%D0%B8%D0%B5_%D0%B4%D0%BD%D0%B8_(%D1%84%D0%B8%D0%BB%D1%8C%D0%BC,_2005)

Maybe so, but even the title of the movie sounds ungrammatical to me.

I corrected. But I think, actually, it's just out of the context. It could be part of "his last days"...

Which is grammatical because possessive pronouns are in the same grammatical class as definite articles.

OK, thanks)