The priest makes it clear how it is to the confesser. The perp knows he is not forgiven if he does not follow through. Committers of crimes usually do not go to Confession if they intend to not make amends. Those that do find out only that they are not forgiven if they do not make amends. Some actually go out of confession and make their repayments and or go to the relevant authorities and there confess civilly. They would be less likely to make that trip if they did not confess to the priest.
Not Catholic so your response is very enlightening. I wonder, what is the policy on confession of ongoing or future crimes?