In this case, it seems that from your own financial situation point of view, it is better to get foreclosed:
1. The house price is likely to drop another $100K.
2. If you rent, you can save a considerable amount of money every month.
3. You will probably need 10 years or more for inflation to catch up, allowing your property to become cashflow positive.
But you said that your intent was a home not an investment. So the final decision depends on whether you can still afford the house given your wife’s unemployment. If you can’t afford (e.g. mortgage is over 40% of your income), you can’t afford. Walk away is the only solution.