I have an old PlayStation One game CD that has music on it that I want to save on my PC. How do I find and extract audio data from it?
Many of the PS1 CDs have audio tracks like regular audio CDs. If that is the case, then regular "ripping" tools such as cdparanoia or EAC may be used.
If the game studio have not yet perished, I would send them an e-mail asking for assistance in this particular case. If you manage to convince them that the audio is going to be used for personal purposes, it is reasonable to hope that they might provide you with information or even tools for extracting the audio.
Apart from that, there is this thread where someone has found a tool that may be working, but it's not likely to be applicable to your game because I doubt that there is a standard way to package PS1 games.