Word for a parasite except that it has no effect on the host

Solution 1:

A host/commensal relationship.

Commensalism:

is a long-term biological interaction (symbiosis) in which members of one species gain benefits while those of the other species neither benefit nor are harmed.

Composed of the two:

The commensal (the species that benefits from the association) may obtain nutrients, shelter, support, or locomotion from the host species, which is substantially unaffected.

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