In the sentence, “The dog gave me, who feeds him, a lick”, feeds does not agree with the person of the antecedent to who. I know that a verb used with a relative pronoun has the same number and person as the noun or pronoun to which the relative refers. Me is first person, yet it sounds incorrect to write, “The dog gave me, who feed him [I feed him], a lick”. What is my problem?
The verb of the subordinate clause (to feed) should agree with the noun in the same clause (who). Not with the indirect object of the main clause (me). Also, 'who' is, in my opinion, a strange relative pronoun to use for this sentence. I'd use 'the one' in this case.