The fact of such non-payment shall not in any way affect the permission to go, if it is not identified or the court has not begun the case for their consideration. First, you need to familiarize yourself with the Federal Law "On the procedure for exit from Russian Federation and entry into the Russian Federation".
Not to doubt and to learn, whether imposed limitations on you in leaving the Russian Federation will address to all bailiffs in the area, as well as to the U.S. marshals service at the former place of residence and stay.

Ensure that in case you pay the fines, the paperwork was sent to the bailiffs. Such a small misunderstanding could prevent you from getting the permit.
If you still have any of non-payment, and the court is not notified and no appropriate papers, you are free to leave the borders of Russia. Be careful if you offer to pay all fines on the spot. This does not mean that will be filled all the papers. The avaricious pays twice. When paying the fines imposed by the court, take the same bailiff service certificate of redemption of nonpayment. Please be patient. The certificate will be issued about a month.
Many citizens are very worried about outstanding loans, which following their departure, will be paid, for example, their relatives. Loans ― is your relationship with the Bank and not with the court. In practice, failure to comply with agreements between the Bank and the individual never affect resolution of check out.

Having a certificate stating that your fines repaid (or you have no actual non-payment), you can safely go on a trip.