Oh boy, what a difficult position to be in!
When my parents went through something similar with me as a child, they rehomed our cat with my grandparents. Do you have a nearby relative or family member who can take your cat in?
Otherwise, unfortunately, I think you may have no choice but to surrender the cats to a shelter. The good news is that there are people who adopt older cats...we got our 7 year old girls on New Year's Day.