A lawsuit filed this year in United States District Court on behalf of eight plaintiffs who faced termination from the program seeks to allow participants with disabilities as defined by the Americans With Disabilities Act to renew at the same rent levels even if they miss the deadline.

The suit claims that many participants are cut off when they miss renewal deadlines beyond the six-month grace period and are asked to file a new application. But when they rejoin the program, the lawsuit said, their rents are frozen at the rate the apartment goes for at that time, which is often hundreds of dollars more and unaffordable for the tenants.

Typically, the tenants do not realize they have been dropped from the program until many months later, when a landlord takes them to Housing Court for nonpayment of rent and seeks an eviction, the plaintiff’s lawyers said.

Officials with the city’s Finance Department, which administers the program, said they had listened to the concerns and had started to revise their rules. This year, the officials said, the department extended renewal deadlines if the tenant has been hospitalized, has been a victim of a natural catastrophe, has been declared incompetent or had a guardian appointed, or has been formally given a diagnosis of Alzheimer’s or dementia.

After advocates complained that the bar was still too high for what constitutes “good cause” because not everyone incapable of meeting deadlines is hospitalized or has the required mental conditions, for example, officials said they had started to waive renewal deadlines for participants who claim a disability under the Americans With Disabilities Act.