One other thing that occurred to me: it's only a worry in an up market where there's equity.
Imagine a more common situation today:
Owner owes 150-200k. House is worth 100k.
You buy it for 100, hopefully less.
To get the house back (in New Mexico), the owner needs to come up with the amount owed, all fees and penalties, costs of the foreclosure, AND 10% interest. So they owed way more than it's worth, and then on top of that will owe a bunch extra. Why the heck would they want to redeem that? They'd suddenly be paying 150-200k+ for a property worth maybe 120 (if you fixed it up).
So when you're purchasing you may be able to find out the amount they owed, and if it's way above the fair market value, you know there's almost no chance they'll redeem (there's almost none anyways, because they just won't have the money, or they wouldn't have been foreclosed on in the first place - if they couldn't pay their 1,000 mortgage bill, how are they gonna come up with 150k?, but about a 0% chance they'll pay way more than it's worth to take over a house that was underwater).