I work in Florida only. The laws may differ where you live.
If the rents are high enough to pay the mortgage and it cash flows, keep the house. In other words, keeping the home is ok if you make at least $500 net at the end of the day after paying your mortgage. Net means after all expenses and taxes. You could get a real estate agent or management company to help you with this. Ask what they charge.
You also can short sale the house. This means your you sell your house and the bank will take for less than what's owed. You don't have to be in foreclosure to short sale your house. A short sale shows on your credit as an account paid in full and minor credit damage. Do not do this on your own. Make sure to get a professional to handle the short sale negotiations. The short sale process is completely free for you. If you live in South Florida I will be the professional you want to call. You can visit me at AntlopMiami.com.
You may have questions. There's a lot more to it but I compressed it for the sake of simplicity. I hope it helps!