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Officials also say the cottage affords the agents a level of access to the Biden family they might not have otherwise.

Asked at the time if the Secret Service typically pays rent to protectees, the spokesman said, “It’s a rental property, so we pay rent there.”

According to Mr. Biden’s office, the vice president’s mother lived in the cottage until she died in January 2010. At that time, the Secret Service had been renting properties in the Wilmington area for agents assigned to Mr. Biden’s protective detail.

After his mother’s death, Mr. Biden asked the Secret Service if the agency would be interested in renting the cottage, but the agency declined. Mr. Biden found a private tenant who later moved out, at which point the Secret Service reconsidered the deal and moved in.

The Times submitted an open records request seeking a copy of the lease nearly two years ago along with other records, but officials have yet to respond.

Mr. Biden last year described to reporters what the cottage on his Delaware property looked like before he fixed it up.

“It had a little, tiny barn on it, it was like a big garage,” Mr. Biden said.

“And it was at the top of the driveway, and my brothers said I ‘gingerbreaded’ it up. I put nicer doors on it, and put shutters on the windows so it didn’t look like an old, dilapidated barn when you walked in.”