I was unable to find much information about this issue so it’s either somewhat obscure or I’m terrible at searching for things. Probably both.
I originally ran into this problem when trying to run Firefox in Firejail using the standard Firejail profile for Firefox. Firefox ran fine, except there was no audio. I found that this was a known issue documented here, but unfortunately none of the suggested fixes had any effect. The page states that newer versions of PulseAudio do not exhibit that issue, so that is not really surprising.