Deed transfer and foreclosure....

Through a real estate lawyer who knows foreclosures contact the lender to determine what they will accept to satisfy the mortgage and stop the foreclosure. Many lenders will arrange for the new purchaser to be financed by them as part of the deal. This requires so good negotiating skill but can be accomplished. Consult with a real estate attorney ASAP.

You can assign and assume the mortgage and simultaneously work out a modification, but you will need a skilled foreclosure attorney to assist you in the process. The outcome will depend on your financial circumstances. There are a number of strategies that can be used from using a QuitClaim Deed and Assignment/Assumption Agreement to purchasing the property in a short sale. The particular lender/servicer and all of the surrounding circumstances play into what makes the most sense. Contact a foreclosure attorney right away before the foreclosure process gets too far along.

Your mom does not need to be in NY to convey the parcel to you. That sounds to be the least of your worries. You need to contact an attorney that is knowledgeable about foreclosures and ask for their assistance.