Yes, the digital output can stop working because it’s dirty, and you can fix it by cleaning it.
I had this problem on an older, used Mac Mini that had been in a dusty environment. Sound was fine coming from the computer’s speaker and the analog headphone output jack, but when?a mini toslink optical S/PDIF cable was inserted into the same jack the output was silent.
The Mini was sending a red glow out to the opposite end of the cable but no matter what I connected it to or how I configured the software settings, there was no audio. That cable did work when attached to other Macs.
Because of your question here, I shot compressed air from a can into the audio output jack on the Mini, then used a small plastic tool coated in rubbing alcohol to scrape at the back wall of the jack, as well as a Q-Tip with the cotton removed. Then another shot of compressed air. The digital (and analog) outputs worked perfectly afterward.