Earlier quoted context omitted.
Considering the fact that you have died, that's a nonissue. If you want to leave something for your offspring, make it a priority to pay your house off first.
Your offspring still would get any equity left after paying the remainder of the note. It's not like they confiscate the whole house because you still owe $100,000 on a $250,000 home. But the survivors do have to keep the home out of foreclosure (as in, keeping the payments current)
I can't tell you how often someone's heirs either didn't know or didn't care enough to take care of what was required to keep the mortgage in good standing to sell the property and get the equity out.