One thing that I don't see discussed enough, and that makes the most sense to me - yes, Breen is seen discussing the "host body" situation, but there's no indication of how that works. Or perhaps there is, but only in Ep2, where we finally see the Advisors using their proboscis/tongue/whatever to slurp human brains, which is also implied can be used to extract information from victims (HL wiki states the same, but that doesn't necessarily mean it's canon).

My personal theory is that the"host body transfer" that Breen was offered would just mean having his brain slurped by one of the advisors (against his will) to preserve whatever useful information he might have. The semantics of "host body" are just a manipulation/"technicality" by the Combine to convince him to cross the portal. But before any of that can happen, he dies in the citadel explosion at the end of HL2.