(I'm not sure about the title, but it's the best I can come up with).
On ELU somebody has asked this question about which form of the verb "to be" to use in the frame
She gives a blanket to me who ? cold.
Since neither am nor is sounds right to me, I am left to conclude that, in my idiolect at least, there is no rule that generates a grammatical sentence, and therefore the frame is ungrammatical.
What I mean by contingent grammaticality is that there is nothing intrinsically (Edit:) or intuitively (end edit) ungrammatical about the frame: with any other NP (object NP, if it marks case) in place of me, there is a choice of verb is or are that makes the sentence grammatical. But with this one particular pronoun there is (on my speculative analysis) no choice which makes it grammatical.
Has anybody come across this line of argument before?