The house does not automatically go to the bank. Your mother owns it now, and when she passes away it will be owned by her estate or heirs (depending if she has a trust or leaves a will).
However, at the point of her death, any lien or debt against the home must be paid off. Since it is a reverse mortgage, the heirs will have a chance to decide if they want to keep it or not and they have 6 months to do either. The 6 months period is for ALL reverse mortgages.
This means they can keep the house by paying the loan off by refinancing the loan into their own names (with a regular mortgage, unless they are also seniors and qualify for their own reverse mortgage), or by selling the house themselves and keeping the difference after the bank gets paid off first. You need to be working with the lender as you go through the process of whatever you decide (not wait to make the decision at the 6th month). If you need more time (like in a down market), the lender can give you two 3-month exntensions (this is lender discretion) for a total of one year. If you do not communicate your intentions with the lender, they will begin foreclosure proceedings right away because it takes about 6 months to foreclose anyway and that will give you the same 6 months left in the home you are entitled to after her death.
If it had been a regular mortgage, you do not get 6 months to do anything; regular loans are due immediately (or within a short time). Another advantage of a reverse mortgage is that only the home is liable for the loan. No other asset can be touched nor are the heirs personally liable.
If the home is upside down and not worth selling, or you are unable to refinance because there is insufficient equity, the heirs can sign a Deed in Lieu of Foreclosure which basically gives title to the lender so they can take care of selling the house at whatever price they can get (up to the loan balance) and whatever shortfall there is, the bank takes the hit. The heirs are not responsible for any shortfall.
I specialize in reverse mortgages (CA)