Remove sick trees only if showing extensive butt rot, heart rot, or dead limbs over half of the crown. Their mode of entry is entirely different. To get in, they must tunnel in. Since the house is built on top of the soil in the yard, then termites must first tunnel into the yard before they can tunnel into the house. Therefore, the first line of defense is to eliminate those resources in the yard that attract termites.
Termites are excavatory endoxylophagous insects.
This means that they eat wood and as they eat the wood they create excavated galleries which are their living spaces. In nature, they are found nesting in logs and stumps and establishing a network of soil tunnels over a foraging territory which allows them to utilize a large number of wood items which are accessible and within reach. Where they feed at any particular time depends on a variety of factors such as the temperature and moisture at various potential feeding sites over time. It also depends on biotic conditions such as incursions of ants, fungal pathogens or nematodes. Subterranean termites enter a house by tunneling in from the yard.