What should you do if a client has been missing for a long time?

The most appropriate action to take when a client has been missing for a long time is to contact local hospitals and check emergency contacts. This step is critical because it directly addresses the well-being of the client. By reaching out to local hospitals, you are expanding the search to places where the client may have received medical attention due to an emergency or health crisis. Additionally, checking emergency contacts can provide valuable information on the client's whereabouts or any possible incidents that may have occurred.

Other approaches, such as sending a letter to the last known address, may not yield timely results and could prolong the situation without ensuring the client's safety. Notifying a family member can be useful but may not be as immediate or effective as directly checking for signs of the client in hospitals or emergency situations. Stopping all efforts to make contact is not a responsible approach, as it neglects the possible risks to the client's safety and well-being. Instead, proactive measures like those mentioned in the correct choice are crucial for ensuring the client's safety and for facilitating potential reunification or support.