The $ means end-of-line, not end-of-string

Nope. That's only the case with the option /m enabled. Unless I misunderstand what you mean...? Which is not exactly very clear to me.

I think the OP's problem is that he used /PAT(.*?)$/ and expected to match the final newline as well. As the /$/ does match just before the final newline as well as at the very end of the string, the non-greediness makes it pick the shortest match, thereby leaving the newline alone. Drop the '?' to make it work.