New York State Property Law

I have two separate questions about New York State property law.
1) If a property is foreclosed on for failure to pay taxes, and is then auctioned by the County, and the sale price is less than the amount of tax owed, can the County bill the original owner for the balance of the taxes due?

2) If someone purchases land through a land contract, finishes paying for it but does not ever get the property title changed into his name, and then the land is foreclosed on by the County for failure to pay taxes and then sold at auction, does the purchaser have any recourse?

I hope I stated my questions clearly. I thank you all for your interest and responses.