It doesn't happen very often, but yes termites can eat through a swimming pool liner.
Termites can create small pin-like holes in the swimming pool liner, usually starting just above the waterline on your in-ground swimming pool, on an above-ground pool the damage usually starts in the cove area.
If your swimming pool liner has suspected termite damage, you can try pulling the vinyl swimming pool liner away from the pool wall to see if you can see any noticeable termite trails or tunnels.
Contact a local pest control company to see if they can treat your yard for termites, or you can put down a layer of plastic underneath the swimming pool liner if this is pre-installation concern.
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