When I got my mortgage my lawyer told me it was assumable and that if I allowed someone to assume it I would be liable for one year and then after that it would fully transfer to them. I'm sure this varies from mortgage to mortgage.
The lawyer also said that it would be colossally stupid (not her actual words, she advised strongly against it) to allow someone to assume your mortgage. If they missed the last payment on the mortgage the bank could come after you for the full amount. She said that they have had to deal with banks doing this multiple times.
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