For people with extra cash available, this can be very attractive compared to the low savings rates being paid by banks.
In the example below, the current mortgage is 5% for 30 years after 48 payments of $1,342.05. The owner can refinance for 15 years at 3.37%. If they put $36,000 into the refinance, their payments will be slightly more but the mortgage will be paid off in 15 years. At that same point, if they keep the current mortgage, their unpaid balance will be $136,049.03.
If you have a goal to get your home paid off and have the available funds, a Cash-In Refinance may be just the strategy for you.