Final answer:
The nurse should pursue the daughter's condition as a potential case finding because older adults with chronic illness are more susceptible to tuberculosis.
Step-by-step explanation:
The statement that supports the need for the nurse to pursue the daughter's condition as a potential case finding is: Older adults with chronic illness are more susceptible to tuberculosis.
This statement is relevant because the chronically ill, older client is living with the daughter who exhibits symptoms like being run-down, coughing a lot, and sleeping all the time. These symptoms could potentially indicate tuberculosis, and the fact that the older adult client is more susceptible to tuberculosis due to their chronic illness makes it important for the nurse to investigate the daughter's condition further.
It's important for the nurse to identify and address potential cases of tuberculosis to prevent the spread of the disease and provide appropriate treatment to the affected individuals.