Termites can infest the stems of garden mums growing in containers outdoors. Termites feed on cellulose in wood and require moisture for survival. They also feed on wood mulch used in landscaping. Termites first attack wood that is located close to the soil. As they feed, they excavate galleries in the wood or in this case the woody stem of the garden mum. Termites also can tunnel through inedible materials as they search for food.