Is the 2nd from a seller carry back (which generally eliminates any deficiency judgements)?

Short sale is simply saying that the house is being sold for less than what's currently owed on the current mortgage.Regarding any deficiency balance (the difference from what is owed versus what the property is sold for) , I believe it depends on your state laws/lender requirements whether she can be pursued for a deficiency balance.

It sounds like the homeowner wants to be able to walk away without any hit to their credit and without any potential tax or deficiency concerns.

I am not familiar with New York but many states require "disclosure statements" by the owner stating any know deficiencies in the property, i.e. mold, roof leaks, insurance claims.An estoppel will give you lots of the information you seek and you can make it a part of the contract.  

When that property sold, the original borrower had a deficiency and I had guaranteed a part of the principal, up to my purchase price.

A tax lien that goes thru a proper foreclosure will eliminate all mortgages, judgments (child support, deficiency, etc) and even certain tax liens and government liens.

I suppose they think they can go after a deficiency judgment on the balance, but that's not real smart nor good banking practice. 

@Mindy Jensen  non recourse and a 1099 are completely different things.I think what your asking is does this state allow for a deficiency judgment on a purchase money deed of trust or mortgage I think that's your first question or what your trying to figure out.Most states do however west coast state like CA WA OR NV AZ do not if its OWNER OCC and it was purchase money..

Either way, you will make periodic adjustments based on actual cost changes that have occurred over time, or else you can find yourself deficient on reserves (like many HOAs tend to be).EDIT: Adding this link for discussion of how to perform a "reserve study".http://www.biggerpockets.com/forums/52/topics/75626-maintenance-proportion-of-rent

If the amount received is not enough to pay the amount due then the lender may seek a deficiency against the borrowers and guarantors.