system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: What happens if someone claims they are guilty of a crime, after been found not guilty?
gpt
In the case of a US case.
They remain free, though if they had not been sued in Civil Court they could be out a lot of money.  
Basically once a not-guilty verdict has been passed in criminal court, then they are out. The 5th amendment to the Constitution guarantees them the right not to be put in jeopardy again (this is what it means to forbid 'Double jeopardy'). This was meant to prevent someone from being repeatedly tried over and over till a conviction was made.  
This also means that any evidence acquired after the trial has completed (up to and including an outright confession) may not be used.   
But this only applies to re-opening a criminal case, there is still the Civil court which is treated as a separate thing entirely. Even if you are acquitted in criminal court, you can still be sued in civil court, and lose there. The most famous case is the O.J. Simpson trial, where he won in criminal court, but lost in civil court.  
That being said, if you win in both civil and criminal court, you cannot be taken to trial again for that particular incident.