No. Although you might tolerate termites or carpenter ants for a few days, termites will eventually eat through foundational beams and other integral parts of the home, making it unlivable. The responsibility of other pests can depend on local laws, and we recommend you read about regular pest control in rentals for more information. In the majority of areas, the laws are usually going to lean on the landlord in terms of fixing damage and performing the required inspections to keep termites out of the home.