One of the possible stories Booth may tell the player during the procedure concerns a character conspicuously reminsicent of Chemical Agent, who comes to get the names of his dissolved adversaries engraved on his putrid flesh. Booth, however, mentions that it's been quite a while since his last visit, the implication being Chemical Agent's death at the player's hands. The problem is that Booth hit me up with that story before I had fought in the Arena at all, which makes his apparent disappearance a little premature, but is all in all no big deal.
I do miss the option of recognising who Booth is talking about and gloating about having put the Agent out of his misery though (to be fair I did not bother to test if such an option appears after having actually killed him, so my bad if it already exists).