The adjective fessus (wearied, tired, fatigued, worn out, weak, feeble, infirm) sounds and looks like it could well be a participle. If there is a verb, I would assume it to mean something in the direction of "to weaken" or "to burden". Is there such a verb, or has there ever been one? I found no suitable verb starting with fed- or fet-. The meanings and conjugations of fetare and fetere do not match. The verb fendere could be suitable, but it seems to survive only in compounds (offendere, defendere), and the past participle seems to be fensus.
I know that proving non-existence is hard. If you think there is no such verb, it is perfectly acceptable if you argue why.
This is related to the later question about the difference between fessus and defessus.