As the landlord, you retain the right to evict any tenant, even one with a housing voucher. While we try to avoid evictions, it is between landlord and tenant if a lease agreement is broken in any way. Every tenant who receives a housing voucher is, however, pre-screened for any possible issues and is already prescribed the resources they may need to overcome these problems. You also get the chance to screen tenants based on your own criteria to avoid any miscommunications.There is no evidence to show that voucher holders make more problematic tenants than non-voucher holders. Studies show that most individuals with housing vouchers are long-term tenants, staying 7-8 years on average.