"Hardship" is really meaningless beyond the fact that the bank is more likely to work with you if you lost your job because your dying with no assets and 6 kids versus this being an investment gone bad and you still have assets. Its a factor they will consider - nothing more.

A deed-in-lieu of foreclosure simply short circuits the foreclosure process by directly transferring the property to the bank. Most banks are not willing to do this as they become liable for any debt secured by the property since their loan, where as those debts would have their interest in the property wiped out by foreclosure.

What you should do is teach your kids the value of being responsible and having them make an effort to do everything possible to get the house sold for a much as they can - thus minimizing the liability for them, you and the bank. Once you have an offer in place, you'll need to negotiate with the lien holder, and lenders and try to negotiate the release of those debts in order to complete the sale.

VERY IMPORTANT to note that this "sizeable" lien on the property will have its secured interest wiped out be a foreclosure, so they should be very motivated to work with you to get a sale completed - even if it means accepting less than the amount in full.

Finally, if they won't negotiate so that you can sell the house then bankruptcy is certainly worth consideration. Your kids may even be able to have the lien wiped out in bankruptcy while keeping the house. Certainly would put you in a better position at least.

Lots of issues here, finding competent counsel would likely be a good idea as well.