HOLLYWOOD — The regulars found out the way regulars always do, from a handwritten note taped by the register, and their first question was the only one that mattered to them: was the place going to change?

The diner has served the same stretch off the Boulevard for forty years, a narrow room of red stools and worn booths where the coffee is bottomless and the eggs come the way they have always come. Its founding owners, a husband and wife who ran it from open to close for four decades, sold the business this month and are, at last, retiring. The buyer is a man who has cooked on their line for the better part of twenty years, and his opening promise to the panicked regulars was that he intended to change almost nothing.

“I’m not buying this place to turn it into something else. If I wanted a different restaurant I’d have opened a different restaurant,” said Signe Abernethy, the new owner, who ran the grill through the transition and knows the menu by muscle memory. “The people who eat here don’t want a concept. They want their booth, their usual, and to not have to explain either one. I can keep that. That’s the job.”

The couple who built it said selling to their own cook was the outcome they had hoped for and half-feared they would not get. Restaurants like theirs, thin-margined and tied to a single room, are more often sold to a landlord or a chain, or simply closed when the owners tire. Handing it to someone who already knew the regulars by their orders felt, they said, like the difference between passing something on and letting it end.

The math still has to work. The new owner faces the same pressures that have thinned the corridor’s independent restaurants — rising rent, higher food and labor costs, a customer base that has to count its dollars. He said he would raise a few prices where he had to and leave the rest alone, betting that loyalty is worth more to a place like this than any renovation. Regulars, he noted, forgive a quarter on a cup of coffee. They do not forgive the disappearance of the pie.

The founders will still turn up, they said, though on the customer’s side of the counter now, an adjustment they expect to find strange. One of them admitted he did not quite know what he would do with a Tuesday morning that did not begin with unlocking the door. The other said she planned to sit in a booth and let someone bring her the coffee for once, and to resist, if she could, the urge to get up and refill it herself.

On the first morning under the new owner the room looked exactly as it had the week before. The stools filled by seven, a regular took the seat he has taken for years without being asked, and the grill was going before the sign in the window was even flipped.