It probably depends. I would think that an alien can be deported arbitrarily regardless of anything (having no absolute right to be in the country to begin with, can be rejected arbitrarily at passport control etc.), but usually in a court of law you can't be penalized for "being" something, only for doing or having done something.

From a legal standpoint that's problematic since the government would be imposing a punishment on acts committed outside its jurisdiction--possibly ex post facto as well.

But a lot of countries have laws which say that you can be prosecuted upon your return for doing anything outside of the country which is illegal inside the country.

Western countries generally only invoke extraterrestrial jurisdiction in matters concerning basic human rights. Laws criminalizing sex with minors oversea are arguably domestic implementation of international law. Sexual slavery is not a choice that sovereign states can make.

I don't think extradition counts as a punishment like jail time, it's the revocation of a privilege, but I might well be wrong.