Protection from Lenders

Although NY may be a 'recourse state' that is just the default position if the recourse issue is not mentioned in the loan. The loan documents themselves can toggle the loan to either recourse or non-recourse. Try to shop for a non-recourse loan with no personal guaranties or carve-outs - if you can find one. The market is strong but banks are weary. You will still need to sign an environmental indemnification either way. It depends on the property type being financed, the leverage ratios, and your earning power, the rate offered, and finally the Bank offering the loan. You can also deed the property to an LLC you own and look to take out a mortgage on behalf of the LLC without personal recourse or guarantee which would even further reduce your exposure. Talk to your lawyer.

How likely is this unlikely default?

Without getting into long winded legal description, I don't think you need to worry. Your loan and its language should clearly delineate what the security for this loan will be. I'm working on a purchase right now for example where there is a box thats checked that specifies the property is the collateral for the loan. Best of Luck