My cousin applied for a job at a major discount chain on the recommendation of his landlord whose duaghter works in HR hiring, (I’m sure it was partially selfish – he had lost his job and assisting him in getting a new job would ensure a continued renter, but still appreciated anytime someone wants to help someone else find a job!). Shane had a felony…what I don’t know was whether he admitted it on the application or if it was picked up on the background check-- or if it matters either way. He was ultimately turned down for the job, and the HR rep told her mother that Shane wasn’t hired because he had a felony. The landlord did not ask about or check background when she rented him the place; however, she is now saying that she learned from her daughter that he had a felony and she will not rent to someone with a record and he needs to find another place to live. I would think that would be a privacy violation. Is that allowable?

My understanding of the law is that crime records are public, and anyone can get them about anyone, and that a job application has no expectation of privacy. Privacy laws regarding employment are company policy, not federal or state law, and he wasn't employed by them even if they do have a policy.
Whether the landlady can break his lease, if he has a lease, is another matter. It depends on the writing of the lease, and possibly what state this is in. And of course if he has been on time paying the rent.