The government could repossess your degree by making it illegal to tell people you have it. Since the vast majority of the value of the degree is as a signal to potential employers, repossessing would maybe kind of work?
Under Texas Penal Code 32.52(b)(1)(C), it is a misdemeanour to claim to have a degree (for purposes of employment/etc) if that degree has been revoked. So, if some law was to say that bankruptcy discharge of student loan resulted in degree revocation, and that law applied to you and you knew about it, then it would be a misdemeanour to use that degree in Texas.
Does this violate the 1st Amendment? As far as I'm aware, that provision of the Texas Penal Code has never been struck down on First Amendment grounds.
Probably not if applied extremely narrowly. (If you tried to prosecute someone for saying that they had earned the degree but has it revoked for non-payment of debt, it probably would violate the 1A.)
But, more to the point, that would only matter for most practical purposes for bachelor's degrees (and sometimes for more advanced degrees) if the degree was revoked before one had any substantial record of experienced based on it, since beyond entry level positions most positions rely on a pattern of experience to which a bachelor's degree is a typical (though often not exclusive) entryway, not the degree itself.
IANAL but I sounds like it would depend on what "use that degree" means. Applying to a position that requires that degree? That seems a clear violation. Mentioning on your CV that your degree was revoked due to bankruptcy? That's not exactly claiming you have a degree, and it's definitely not a lie in any form. Can the government really prevent you from telling the truth about your education?
I suspect most companies wouldn't really care if your degree was revoked or not (unless it was revoked for cheating or other non financial reasons)
I think there might still be a way to implement it, something like allowing the court to revoke or annul the degree?
It's also possible that an explicit restriction on telling employers that you once had a degree would work, since we do have other cases where we restrict what people are allowed to ask and tell in job interview situations.
Another possibility is that the court could ask you to promise not to disclose your degree in exchange for granting you bankruptcy relief. Nondisclosure agreements are a thing, so this seems like it's probably legal?
They already did that with the State Secrets Act (or whatever the American version is called) and nondisclosure agreements. (Just to be clear, all three of those are in fact human rights violations, I just don't think anyone who matters cares.)
(Still half jokingly)