Who—the subject pronoun—is correct.
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In order to determine whether the relative pronoun functions as the subject or the object of a clause, we can apply a little test. Let's start with a simpler example:
Richard Nixon—who/m Mazo supported—asked for the series to be terminated.
who Mazo supported --> *Mazo supported he (incorrect; don't use subject pronoun)
whom Mazo supported --> Mazo supported him (correct; use object pronoun)
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Your example is more complex, but let's apply the same test:
Richard Nixon—who/m Mazo claimed had lost the election—asked for the series to be terminated.
whom Mazo claimed had lost the election --> *Mazo claimed had lost the election him (incorrect; don't use object pronoun)
who Mazo claimed had lost the election --> *Mazo claimed had lost the election he (incorrect; don't use subject pronoun)
Well, wait a minute, if neither of those works then . . . we have a clue. The pronoun is the subject of its own clause within the clause:
Richard Nixon—who/m Mazo claimed had lost the election—asked for the series to be terminated.
whom Mazo claimed had lost the election --> Mazo claimed [that] him had lost the election (incorrect; don't use object pronoun)
who Mazo claimed had lost the election --> Mazo claimed [that] he had lost the election (correct; use subject pronoun)