What is the process of buying a foreclosed house with tenants in upstate NY?

Until recently, there was no "tenant foreclosure law(s)"—in New York or elsewhere. Tenants were not parties to the foreclosure and had no rights in it. Indeed, since the foreclosure generally terminated the lease(s), the eviction process could be begun as soon as you, as new owner, took possession of the home. (Though note: tenants in foreclosed properties still had what I call "process rights" in that you had to follow the correct steps to evict them. In particular, there are no "self-help" evictions or simply locking them out.)

However, with the real estate bubble bursting, leading to the mortgage crises, the federal government and some state governments have passed laws to protect innocent renters—people who’ve been paying their rent and abiding by their leases—from being thrown suddenly out of their homes because their landlord doesn’t keep up his mortgage payments.

New York State enacted a law which requires that tenants be allowed to stay in their rentals for at least 90 days—possibly for the entire balance of their lease term. In many ways, it parallels a federal law that was also designed to protect tenants in foreclosure situations, by allowing the tenants to stay in the rental for either 90 days or the balance of their lease terms. (If you were looking to live in the premises yourself, as you seem to be, the 90-day limit applies.)

Obviously, this may affect your plans—you might not want, or be in a position to, wait at least 90 days before forcing out a tenant and moving into the building you purchase. Unfortunately for those who buy homes in foreclosure—though fortunately for tenants who may not have done anything wrong, other than having the bad luck to rent from a landlord who couldn’t or wouldn’t honor his or her financial obligations—new laws have created a "tenant foreclosure law" with tenant foreclosure rights.