Well, again, the encryption system will. Or at least it can. (Apparently you can encrypt without signing? WTF use is that? But let's assume signatures are used.) The MIME structure of email is the problem here. It isn't OpenPGP's problem to solve, which we know because there is literally no way for them to solve it. No conceivable (sensible[1]) update to OpenPGP could fix the problem, so it can't be their responsibility.
[1]: I mean, yeah, they could ship something that hacks the Thunderbird process and gets the rest of the email, but that's just crazy talk. Nothing that has a sensible API that fits with what Thunderbird is doing now can solve the problem.
Is there a standard for this? It seems like if you tried to do it by hand, the receiver's UI would present this in a scary/confusing way. I'm imagining instead some sort of "Alan Smithee" User ID which the UI interprets as "deliberately anonymous/disavowable".
[1]: I mean, yeah, they could ship something that hacks the Thunderbird process and gets the rest of the email, but that's just crazy talk. Nothing that has a sensible API that fits with what Thunderbird is doing now can solve the problem.