It's going to depend a lot on personal situation, but they might not be able to obtain a new loan due to credit assessment, and therefore be stuck with the old one.
Perversely, at least in the UK, a lot of people are paying higher rent than they would be for a mortgage for a similar place, but they can't get a mortgage due to "affordability", despite a demonstrated history of paying the rent.
Similarly, people can be on a 10% mortgage, paying it consistently, but unable to open a new, cheaper mortgage to replace it because their current circumstances don't pass the criteria. Criteria may include age (time to retirement) and current income.
Perversely, at least in the UK, a lot of people are paying higher rent than they would be for a mortgage for a similar place, but they can't get a mortgage due to "affordability", despite a demonstrated history of paying the rent.
Similarly, people can be on a 10% mortgage, paying it consistently, but unable to open a new, cheaper mortgage to replace it because their current circumstances don't pass the criteria. Criteria may include age (time to retirement) and current income.