What happens depends on the country.

US law says expressly that nothing changes (US federal law, US Code Title 1, § 109. "Repeal of statutes as affecting existing liabilities") unless the law specifically states that it does (some laws have done so in the past). However, that's Common law (the fundamental principle of law as applied by states descended from the British empire).

If we instead look at countries which use Napoleonic code (law based on humanist principles), they use the principle of "Lex Mitior" (the milder law). Under the milder law any change in law is supposed to benefit the accused rather than the state. So in many countries that base their law on the Code Napoleon (notably France, but really most of the EU) when a law is repealed that triggers an automatic sentence review, and if it's no longer a crime "Hey hop, you're free to go".

P.S (maybe not so ELI5): "Hey hop, you're free to go" is in practice a bit more complicated than that. Many countries that practice Lex Mitior also practice "Socialism!". So before ratification (when it's signed by parliament/congress/whatever) and long before implementation (when the law goes into effect) the law is sent out for consultation. The prison system and social services get to say "Hey, no biggie. We can deal with this relatively quickly" or "uh. We're going to need X months to prepare for that, because this is huge". So on the day the law is ratified (signed) the bureaucracy gets to work. Sentences are reviewed, prisoners are scheduled for release, social services are notified so that they can set up the ground works (sending people out with no housing, no money and no social network would be a recipe for catastrophe) , relatives are notified etc so that when it's implementation day everything is set and people can be released in an orderly and humane manner.