First came Hurricane Sandy, which left her homeless for a time.

Then came the live-in boyfriend, who battered her.

Now the 44-year-old mother of three young children is homeless again, forced into a shelter by the abuse and trapped there by poverty and the paucity of living options in a city woefully short on affordable housing.

She worked as a hairdresser and her clients were in her old neighborhood. But so was the ex-boyfriend, said the woman, who spoke on the condition of anonymity.

“My best bet,” she said, “is not to go back.”

Having walked away, victims of abuse are often left with no place to live and little means of support, and frequently end up homeless. In New York, this has helped drive the shelter population to a record high, with more than a quarter of all families in shelters citing abuse as the cause for their stay, city officials said. And, nationwide, many cities report a similar experience.