If you _do_ break up, this also makes it harder for one person to keep the house, which might be bad if there's kids in a local school, etc. If you have 100k in equity it's easier to buy out your ex than if you have 1 million in equity.
While the bank holds the title on a financed car, they don't actually hold title on your house. They will have a recorded lien, of course. But you hold the title, which should help you sleep ;p.
That's why a house is foreclosed, and a car is repossessed. Repo is lender calls the tow peeps and they pick up your car; foreclosure requires notice and often court and plenty of bureaucracy.
Neither option is fun, of course.
On topic, I was paying a little extra on my mortgage (mostly as I rate adjusted down, I would tend to keep paying the old payment), but when savings interest is more than mortgage interest, it was just as easy to sleep with a savings balance equal to the mortgage balacne as with no mortgage.
Or to put it a different way, if my house was paid for, it would hurt, but I could make all ends meet just working fast food jobs. It wouldn't be an easy life, I'd end up walking a few miles to the nearest fast food place because I couldn't afford a car, but I could at least keep my house.