The answer is very specific to your contract - but a general management agreement only entitles one to payment upon delivery of renter. Look for foreclosure options as opposed to simply letting the property go. It may be easier on your credit.
Your obligations to the management company will be determined by the terms of the contract you entered into with them. To avoid foreclosure, you have to pay the mortgage. Keep in mind, you do not foreclose, the lender forecloses on you. Your question is really short on some very important facts so it is hard to give you more than general information. I suggest you consult an attorney in the state where the house/ management company is located to get a better answer.
Have an attorney review the contract. Why was he/she unable to find a renter?
If they breached the contract because they simply put your file on the shelf and did not do any advertising, etc., then you may have a cause of action.