Hannah Kirshner and her boyfriend, Hiroshi Kumagai, looked at several rental apartments last week. One was missing a couple of floorboards, and the empty spaces had been filled in with rocks. Another had a narrow spiral staircase leading to the bedroom, which the real estate agent repeatedly referred to as “death stairs.”

“It smells like pot,” Mr. Kumagai said upon entering that apartment. The agent agreed.

In the best of circumstances, trying to find a rental in New York City is like taking a very expensive and stressful trip to the dentist. But Ms. Kirshner and Mr. Kumagai are not in the best of circumstances: they are among the thousands of New Yorkers who were displaced by Hurricane Sandy, which filled their garden-level rental apartment in Red Hook, Brooklyn, with water just a few inches shy of the ceiling and rendered it uninhabitable for months.

So they are now searching for a new rental and facing a variety of challenges, including a budget strained by so much ruin, and competition from other renters displaced by the storm. But there is a special wrinkle in their quest for a new home.

“My chickens bring me a lot of joy, but I know we have to be realistic,” Ms. Kirshner said.

“But man,” she continued, “it would be nice” to be able to keep them.