What happens to the copyright of that code? 1. Does it get transferred to the shareholders, who would then all have to agree with each other to be able to relicense one day? 2. Does it fall into public domain? 3. The copyright is transferred to the state? 4. It falls into some no man's land and never can be relicensed? 5. Maybe that's a question that must get an explicit answer as part of the winding down procedure? 6. Something else?
The copyright is held until it expires. If the code is explicitly GPL, then you can still use it - but you can't change the license or remove the copyright, and you have to abide by the clauses in the GPL version used. There are organizations that might sue to enforce the GPL license, even if the original copyright holders might not because they are defunct.
Note that someone owns that copyright, because someone owns the IPR of that company, even if it is defunct. It might be worth checking to see what company bought their intellectual property, or who the founders are (they may be the IPR holders too). It's a big longshot, but you might get permission to relicense the code under a different Open Source license, or a transfer of the copyright.
Do you want to use the GPL project?
Do you want to modify and redistribute the GPL project?
Do you want to modify and redistribute the project using other license like MIT or closed source?