Under GPLv2, if you violate the terms, you lose the license, meaning that you can no longer copy or modify the work at all, and there is nothing in the GPL (v2) itself to get the license back. However, the copyright holder can forgive the violation and reinstate the license.
Likewise, under GPLv3 the copyright holder can give you additional shots to get the license back.
It's important to remember that the copyright holder's powers go beyond the terms. This does create problems for projects with hundreds of copyright owners, like Linux: if you violate the copyright, you apparently need the forgiveness of every Linux copyright owner, or, in the case of the dead contributors, their heirs, or you can never distribute a Linux kernel again (I suppose you could try to make a cut-down kernel without the contributions of the more unforgiving developers). Some might see this as a feature rather than a bug, though.
GPL code can import BSD code; it's only improper if the copyright notices are stripped off (which has happened, so you're right about that).