The fate of the few residents should the Prince close is unclear.

“Any hotel is going to have something sometimes,” she said. “But you don’t go off the deep end with it, ‘Oh, we have to close it down!’ Where do we go from here? Where do we go with high rents?”

In the past two years, there have been 70 calls to 911 involving the address, according to the New York Police Department, for complaints that included fights and disorderly persons. “Every iteration of the neighborhood for the past couple of decades has had a problem with this place,” said Justin Brannan, 37, a lifelong resident who, like many, has called for the hotel to shape up or close.

The Prince drew renewed attention when the city announced plans for a new prekindergarten on 93rd Street, just a few steps from the Prince, leading to fears of small children mingling with the people that the hotel supposedly draws.

In February, Mayor de Blasio held a town-hall-style session in Bay Ridge. During the meeting, a resident asked what steps the mayor was taking about the Prince — the hotel had been under investigation for months following a concerted push by Community Board 10, which for years has compiled a dossier of the Prince’s problems. A day after the session, deputies from the Brooklyn sheriff’s office raided the building, for which nearly $400,000 is owed for code violations, according to the city’s Finance Department.

The auction, scheduled for June 8, is intended to ensure that the city is paid what it is owed, and possibly to lead to the replacement of the Prince.

For now, the hotel, with its pretty lobby of chandeliers and ceiling fresco of the zodiac in gold, is still operating, advertising rates of $75 to $95 a night, and receiving a polarized mix of pleased and disgusted reviews from customers on rating sites like Yelp.