Even if an employer learns what it believes to be the new mailing address for a terminated employee with a balance, doesn't that participant have to (must) take action to provide instructions to the employer or recordkeeper to change their mailing address? Otherwise, there could be privacy violations, etc.?
You should review the many prior discussion threads for more ideas and concerns. A search term of "missing" might be helpful.
Probably an important part of this process is interviewing current and former employees who know/knew the missing employee. Perhaps interviewing former neighbors. This step is likely undertaken by the employer (not by any TPA). Because the plan sponsor wants a real answer, do not be sucked in by the "last known mailing address" excuse; this is (in very practical terms) a "cop-out". And the sponsor should eventually be prepared to deal with a response similar to "returned to his/her home country".
There are companies that provide this service (of finding terminated employees). I don't recall any names, but your TPA/Service Provider may have some names handy.