Do plan sponsors or their service providers allow participants to convert their loans to coupon payment upon termination?

It depends. Some plans call for the loan to be paid off on termination, or it becomes a distributable event.

I had a client where, when a participant terminated, their loan converted from payroll deductions to a monthly personal check. It was the participant's responsibility to send the check in on a timely basis, to an address provided by the client (which was our office). If the payment was more than 5 days late, our office sent out a reminder. If payment was not received in 30 days, another reminder was sent. If not received in 60 days, the loan was defaulted. I would have preferred a payment booklet, but that was not a service that we provided.

If the client is willing to pay for a payment "book", I would go that way. This is assuming the client wants to allow terminated employees to continue making loan repayments, and wants the burden of chasing someone down when they go into default. The best thing to do, in my opinion, is to make the participant pay the loan off upon their termination, thus eliminating future headaches.