I get that part but again he's going to want a signing bonus and we would be responsible for any signing bonus if he was traded which makes no sense on our end.
If this was such a plausible idea then somebody could cite examples of it happening in the past.
If we franchise tag hardy and trade him away, then he becomes someone else's problem entirely. We take no cap hit, they take on his franchise tag money, and they renegotiate to a deal they find suitable, then they are responsible for ALL of that new contract, we are on the hook for nothing. It's a pipe dream, and oh so glorious, it's just not very likely.
unless you are talking about giving him an actual contract and not the franchise tag, then, yes, we would be responsible for some of the money if we were to then trade him away.