In 2015, disabled people in shelter sued DHS in a federal class action lawsuit called Butler v. City of New York 15-CV-3783 (RWS) (JLC). This is a Class Action case, which means that it was brought on behalf of a group of people. Both sides in the case want to settle it now, and have asked the judge to approve their settlement. In the settlement, DHS has agreed to make sure people with disabilities can get shelter. DHS has also agreed to change some of its rules to better help people with disabilities.
https://www.coalitionforthehomeless.org/get-help/disability-accommodation-2/butler-notice-en/