Texas lawmakers want state to find a way to halt evictions until backlogged rental relief is sent Texas lawmakers want state to find a way to halt evictions until backlogged rental relief is sent The Texas Apartment Association is still directing its members to abide by a CDC eviction moratorium, but acknowledges property owners are in a tough place. Protestors place furniture and rally outside of the office of Senator John Cornyn on Sept. 1, 2020 in Dallas.(Juan Figueroa / Staff Photographer) The Texas legislature wants the state agency handling federal rent relief distribution to find a way to halt eviction proceedings while it works through a backlog of requested relief payments.