“It’s a building that’s just sitting there,” said Harold Vroman, chairman of the board of supervisors in Schoharie County, where Mr. Cuomo shut down a 100-bed minimum-security prison last year. “Who wants to buy a jail, you know?”

Other states offer some encouraging examples. In Massachusetts, the old Charles Street Jail in Boston was transformed into the Liberty Hotel, which opened in 2007 and embraces its history — among the offerings at one of its bars, Alibi, is a $12 blueberry mojito called the Jailbait. And three years ago in New Jersey, the cells were removed from a former county jail in Newark and the building was converted into government office space.

But those buildings were jails, which are often smaller, grander and more centrally located than prisons.

“Those ones, like old courthouses, have a future life,” said Elizabeth Minnis, chairwoman of the American Institute of Architects’ advisory group for correctional facilities, courthouses and law-enforcement buildings. “But the stuff out in the middle of nowhere, it probably has nothing. You’re going to have to just try to get it off your books. It’s almost worth paying somebody to take it off your hands or give it away for free, because it becomes a liability.”

Consider the Oneida Correctional Facility, a 998-bed medium-security prison in Rome that closed last October. It shares utilities with a rather unattractive neighbor: another state prison.

“The only possible thing that you could use this for would be for government or military,” said Fred Macchia, a commercial real-estate broker in Rome. “You couldn’t make it into a hotel. You couldn’t make it into an apartment complex. You’re talking millions of dollars to renovate. Who’s going to do it? The state’s not going to do it — they’re trying to get rid of it.”

All three prisons closed by Mr. Paterson are vacant. One was mentioned as a possible test site for hydraulic fracturing, the much-debated method of extracting natural gas. Another, Camp Gabriels — a minimum-security prison in Brighton, in the Adirondacks, that was originally built as a sanitarium for tuberculosis patients — has twice been put up for auction, first with a minimum price of $950,000, and then with a $750,000 minimum. No one bid either time.