I was taught that it is likely that as a condition, it is likely that the priest would tell them that they would have to turn themselves into the police.
So it is unlikely that a person would leave the confessional by simply saying a few “Hail Mary’s” and get on with their life. Priests know that Justice needs to be served here on earth too, crimes need to be solved and that victims and their families need closure.
Therefore if the person going to confession did not turn themselves in, they would not be receiving the grace of confession and absolution, this is my understanding anyway. Remember this is God we are talking about too, with God there are no loopholes! Hope this helps. God bless you.