That's true if you've been convicted and sentenced for the crime regarding which your testimony would self-incriminate, but not otherwise. Someone who has committed the crime but hasn't yet been convicted and sentenced still falls under its protection, assuming there isn't a grant of immunity from prosecution to force the testimony anyway.

Other way around, sadly:

https://en.m.wikipedia.org/wiki/Haynes_v._United_States

Convicted felons are exempt from the portion of the National Firearms Act that requires that machine guns (and other NFA items like short barreled shotguns) be registered as it would violate their 5th Amendment rights.

Huh, that is one of the most interesting supreme court decisions I think I've read. I kind of agree with it in a text-of-the-law sense.

I would be very curious to see that logic hold up in court these days. They got Al Capone on tax evasion for instance, but wouldn't paying his taxes on ill-got funds have been incriminating?

and in any sane legal system you are innocent until proven guilty.