What happens if you take the fall for a crime you didn’t do?

If the DA has enough evidence to prove that, both prove that you lied and that the other person is guilty, then the DA goes to the judge, petitions to have your conviction vacated, and then prosecutes you both, your friend for the original crime and you for obstruction of justice and perjury. This does happen, but when it happens, DA's don't just take people's word for it. There has to be compelling evidence to get them to go down this road.

you should not purger yourself under oath. that in itself is a crime

RIP

You go to prison. You admit the crime, you do the time. DA doesn't care as long as the courts are cleared.

After the jury decision, it is final. Only if the criminal uses the court process to appeal that decision will anything else happen. If the criminal does not appeal, it is what it is. So, there is no way or process for anyone to discover you lied. And you proving you lied is really hard and much more expensive, especially from jail.

In the UK you'd get done for the perversion of justice