All searches in Splunk are run as their own processes. When you issue a search, Splunk will create a new process responsible for handling that. If you kill that process, the search will not complete or return any results, and Splunk will return an error message saying the process was canceled (iirc). From this it follows naturally that these processes are not the kind of processes that are expected to be running constantly, so there is nothing that needs to be explicitly "started" if it is "stopped".