Global search finds people, organizations, tasks and reports. A prefix narrows the result category: use a people search for a worker, an organization search for a supervisory organization, and task or report searches for actions and saved reports. You can search part of a name, but a partial match doesn't establish identity.
Read the result category and worker ID before opening a record. A worker can remain searchable after termination because historical reporting still needs that person. No matches may mean the prefix is too narrow, the text is misspelled or your role can't see the object. Remove unnecessary words before assuming the record is absent.