I am really sorry to hear about the outcome of your home.
New York State does not permit property owners the right to redemption, or put another way, the right to re-purchase the home from them after it was sold at a courthouse auction.
As for the tenant, if the buyer was the bank that repurchased, they will begin eviction proceedings. If the buyer was an individual or other entity, they will also begin eviction proceedings against JOHN and or JANE DOE.
Absent an executed lease agreement, they are subject to the legality of the lease agreement in the eyes of the court.
By the way, it's generally a bad idea to ask for legal advice on an internet forum.
Tough to hear about situations like yours. You mentioned you were totally unaware of their intentions, were you also unaware the payments were not being made on the property? This may seem like a silly question, however I do know of property managers that handle such finances (Mortgage Payments) for Landlords; we are not exactly clear on why they foreclosed on your home other than the obvious. Can you please offer any other explanation?
Some states have a redemption period in whcih a foreclosed owner may buy back the property. Only an attorney can advise you how your state's laws would apply to your situation.
Your tenant has probably about 30 days since they/you could force the new owner to formally evict them in court. Your tenant might also make some money off this ordeal if the new owner offers them cash to get out now, which is becoming customary.
I really hope you weren't taking money from the tenant and not forwarding it to the bank to pay the mortgage...I wonder if your tenant would have a legal claim against you if this were the case...