@Wesley I. Yes to all! It depends on the note, the payor's situation, and how much of a discount the note was purchased at. Many of the notes we buy have a face rate over 6% so it is easy to show them the kind of savings they would get over a 15 or 30 year term in the current under 3% mortgage refinance rate.
If that is not enough motivation we have offered the incentive of a discounted payoff. For example on a $100,000 note we might offer a 5% discount of $5,000 if they payoff in full in the next 90 days. The numbers have to work and it depends on how much discount we have from the initial purchase of the note. We did that on note in Oregon last year that worked out well.
If you work with a servicer that reports to the credit bureaus then you can help the buyer/payor either establish credit or improve their credit with timely payments. This will help them qualify for a refinance at better rates. A good relationship with a loan officer can help as well.
Yes, we do work with the servicer. They have to be part of knowing there is a discounted payoff. Depending on the servicer they may or may not want to be part of the initial discussion. You definitely want to involve them and play by their rules. Their job is to help keep you safe and compliant in the servicing and debt collection arena.