Since unemployment is a bit of trouble, and one must do things, such as work searches and weekly certifications in order to get the money, a lot of people think it would be less trouble to simply say, "Others need it more than I...." and eke out their survival in other ways. They also think they are getting points for nobility, refusing to take a "hand out." But in reality, it's the requirements, the trouble involved in getting the benefits that cause most noble refusals.
In many states, qualification for any sort of income assisted or based services require that if a person is discharged or laid off or voluntarily quits a job, they have to go through the process of filing for unemployment benefits. This is both in order to keep receiving the level of services they have in the past, and in order to receive on-going services such as Food Stamps, low income housing assistance, or Medicaid, or aid for dependent children.
Unemployment insurance is not income based, or considered a finance support program. It would be as dumb to refuse it if laid off as to say "I elect not to receive my social security retirement, but I want you to classify me as low income anyhow and give me the services I need based on my income without my using this money."
While you can elect to be this dumb personally, you can't do it and still receive low income assistance of any kind based on state grants if such is the regulation in your state. What your landlord in this subsidized housing would do is not calculate your income based on what you would be getting, he has no access to the amount of your claim or even whether or not you would be qualified. But he can, if the subsidized housing is part of the state income support system, require you to go through the process of filing for your benefits or face eviction procedings. When you receive income subsidies, you are forced to comply with their regulations.