Sort of. Cryptics, which are the international style, might have a clue like "insect in pants" -> "ant", which is pants without the first and last letters.

And more complicated variants, like anagrams, mashing words together, etc.

You could have a pun in the answer - although I think that's pretty rare - but the answer itself would still need to be a recognized word/phrase.

That's really interesting—I'm not much of a crosswords fan, but I had never even considered the idea that there are "dialects" in what crosswords clues & answers could be.