Let's consider a language where even the first person singular pronoun is marked for gender. Now, this can provide an interesting situation with regards to reported speech.
Obviously, a person can report speech from a person of the same gender, or of the other gender. With the other gender, one could keep using the first person pronoun - but alter the gender marking - and still be entirely clear who one is speaking about.
With the same gender, however, one might be expected to replace first person pronouns with third person pronouns of the same gender.
Thus "She told me(masc) she doesn't like roses" comes out as "She told me(masc) I(fem) don't like roses", but "He told me he doesn't like her" comes out as "He told me he doesn't like her".
Of course, one could permit for the ambiguous system where first person is used in both. One could of course also consider a system where first person in embedded contexts can be "restored" by reduplication:
Where in a), it's me not knowing what I am talking about and in b) it's he who doesn't know.a) he told me I-I don't know what I-I am talking about vs.
b) he told me I don't know what I am talking about