The answer to your question is yes, but why would you want to reinstate the defaulting loan if the loan balance is more than the home is worth. Typically most homes going into foreclosure in your area have a higher mortgage balance than their current market value. Additionally, if the loan is in default, then I'm sure the HOA dues (if there is an HOA) is behind, as well as possibly the taxes.
If you wish to and the defaulting borrower will work with you, you can bring the loan current and refinance out to pay off the loan, that is if you have the means to do that.
You should consult with a real estate attorney for your advise on how to best handle this situation.
I wish you the best of luck resolving this.
There are many other options you can pursue if you desire is to stay in the home.
Anyone with the funds can bring home payments current, whether or not they're on the deed. So long as the bank gets the money, that's all that matters.
And if someone's on the deed, there's even more reason (generally) to bring the loan current.
And as Dp2 says, that's a technique that some investors use. (And it generally works out to a win-win-win solution. The investor makes a profit, the homeowner doesn't further injure his/her credit, and the bank gets its money.)
Hope that helps.