I can't remember whether Filch was even mentioned during the last book.
Given the Ministry's strong rules against Muggle-borns, it could be assumed they might have somehow tried to dispose of squibs as well, but it seems unlikely, since at least in the school he would be under the teachers' protection.
Was he a participant during or before the battle of Hogwarts? I vaguely remember Mrs. Norris being mentioned somewhere during the battle, but not Filch. Did he escape, hide or fight with the wizards? Is it mentioned anywhere what happened to him after the battle?
PS: I have seen this where it says he helped students escape, but does not cite any references, and might even be describing the movie. If Filch is indeed mentioned in the last book, please provide the relevant quotes.