The reverse mortgage would have to be paid off if/when title is transferred out of your mom’s name, anyone is added to title, or your mom moves out. You could buy it from her, paying off the reverse with the proceeds of your new mortgage (assuming you don’t have cash to do so). She can’t, however, just convey her ownership interest to you via a quit claim deed as the reverse mortgage would then be due and immediately payable.
Perhaps another option to consider is to have your mom “sell” the property to you subject to the mortgage. You could then rent out the apartment and you would collect the rent. You could then use your income to help your mom. Whether or not this would violate social security would be an issue to ask your attorney.