Normally when a first mortgage is paid off the second moves into the first position unless the holder agrees to "subordinate" the second. A subordination agreement is an instrument that allows a first lien or interest to be paid off and allows another first mortgage company to come in and be the first priority lien holder.
It is very common for the borrower to pay subordination fees. The second mortgage belongs to the borrower and most likely it is the borrower requesting to keep it open. Most banks handling a refinance would rather you pay-off the second mortgage rather than subordinate.
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