This article answers some common questions about subleasing and each party's rights in a sublease agreement. Responsibilities: The sublessee is responsible for paying rent to the original tenant (sublessor) as stipulated in the sublease agreement.Obey (a) all applicable laws relating to the use, condition, and occupancy of the Sublease. Here is a sample sublease agreement you can fill out or use as a template. A Texas sublease agreement allows the original tenant to rent out all or part of a property to a new tenant or subtenant. The trial court granted summary judgment for the leasing agent, and the lessor appeals.