Can a tidally-locked planet have a long term natural satellite?

Approximately how likely is it that a tidally locked planet would have a long term natural satellite, and where would that satellite most likely be located? What I've so far researched (and puzzled out on my own) indicates it would be extremely unlikely and would either follow the terminator line or be opposite the star and orbiting at such a pace as to be geosynchronous.

Additionally, would it be feasible to place a man-made satellite at such a planet, assuming fuel/spacefaring technology has not progressed too much (I have another explanation for traveling from one system to another) and considering the fuel requirements to keep the satellite in orbit?

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Can a tidally-locked planet have a long term natural satellite?

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