Felons have trouble renting apartments because landlords often conduct criminal background checks on potential renters. Many landlords have a policy of not renting to felons, even if their conviction has no reflection on their ability to pay rent.
A smaller subset of landlords openly welcomes felons. Due to the difficulty most felons have finding housing, these landlords decide to take them in and disregard any sort of background check. Often these landlords are open about their willingness to forgo background checks, and they often forgo other sorts of background checks, such as credit checks, that typically disbar felons and others from finding housing.
Lying about a felony also is sufficient grounds to deny an applicant the opportunity to rent. Some people with felonies lie about their status on applications in order to avoid the stigma against people with felonies. Once their prospective landlords learn about their convictions and realize they liked, these applicants typically have their applications to rent denied.
Prisons also release prisoners on unannounced dates, making finding housing prior to exiting prison an impossibility. In addition, felons often find their personal networks of contacts have shrunk immensely during their prison stay, contributing to the difficulty in finding and renting an apartment.