I believe it is fairly well understood that you cannot link proprietary code to code licensed under the GPL because you're creating a derivative work and have to license it all under the GPL. Tangentially discussed here. I was researching FOSS license exceptions and came across the GPL linking exception defined here in FSF's FAQ. At first I misunderstood the direction of this and thought it sounded like LGPL or something like the class path exception.
If you want your program to link against a library not covered by the system library exception, you need to provide permission to do that. Below are two example license notices that you can use to do that; one for GPLv3, and the other for GPLv2. In either case, you should put this text in each file to which you are granting this permission.
Only the copyright holders for the program can legally release their software under these terms. If you wrote the whole program yourself, [...] you are the copyright holder—so you can authorize the exception. But if you want to use parts of other GPL-covered programs by other authors in your code, you cannot authorize the exception for them. You have to get the approval of the copyright holders of those programs.
When other people modify the program, they do not have to make the same exception for their code—it is their choice whether to do so.
Because you can violate your own license and copyrights, let's make a more relevant example. I am not the sole copyright holder of GNU Emacs which is licensed under GPL version 3 or later. Because of this, I cannot distribute a modified version linking to proprietary, closed source libraries because I cannot make the linking exception. But why? Why do I need the exception? Is it just because the concept of linking is not directed and I cannot legally relicense the proprietary, closed source code?
Does this change for "source available" type code at all?
I feel pretty confident about the answer to this but I haven't been able to find a good question about this nor do I have a good context on why.