I think this depends on how exactly the copyright infringement is settled. I am not a lawyer, and this is not legal advice.
The copyright holder may sue you for damages, and still require you to come into compliance with the GPL. Depending on which version of the GPL you are using, the copyright holder may have to explicitly give you permission to resume distributing your software (presumably after they have verified you are now in compliance with the license). I believe other versions of the GPL (version 3 I think) allow you to have your rights restored immediately if you come into compliance with the license (only for first time offenses).
Another way damages might be paid would be for the copyright holder holder to grant you an exception in exchange for something. This might mean that the copyright holder allows you to use their software in your closed-source/proprietary program in exchange for money (e.g. royalties or some other fee), advertising, developing another piece of software for them, doing chores around the house, etc. The copyright holder can chose to license their software however they please, so it's really up to them how/if they grant you an exception. If the copyright holder is your best friend, they may just grant you the exception to use their software however you want without having to pay any real "damages".
An example of using the GPL with an exception from the copyright holders would be the GNU Classpath: https://www.gnu.org/software/classpath/license.html
GCC Runtime Library Exception: https://www.gnu.org/licenses/gcc-exception-3.1.en.html
I'm fully in support of open source software and believe everyone benefits when code is publicly available.
Just to play devils advocate here: Sure, nothing forces you to release your proprietary code under the GPL if you have a derivative work and you are not in compliance with the license. You could certainly just stop distributing the software you have spent years developing, cost you millions of dollars to develop, and your business depends on it. So while you are not "forced" to license your formerly proprietary software under the GPL, companies are often left with very few options to remedy the situation (and continue distributing their proprietary software). Depending on who the copyright holder is on the dependent GPL software, you may be able to get an exception from the copyright holder (possibly in exchange for money). If you're unable to get an exception, your only options are to either stop distributing your license-infringing software or release your software under the GPL.