It sounds to me like you have DC (direct current, not AC, alternating current) going to your speaker. If you were to graph it, normal AC is what a speaker expects. The cone pushes forward and pulls back, at rest it’s at “zero”. With a DC offset, at rest is no longer at zero, it’s either idling pushing out or pulling in. This is very hard on a speaker motor, it will eventually overheat the voice coil and die.
If my guess is right you’d see it in a waveform editor like Audacity and it would be whatever sound file you’re feeding the RPi. Perhaps when you paused it went to pushing out a DC signal?
Of course that’s just an off-the-cuff answer.
KO
P.S. Welcome aboard!
Added: While walking my dog, I tried to think of tests.
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A multimeter across the terminals of the amplifier would show you DC, but not everyone has a multimeter available to them.
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Get the system into paused state, disconnect the speaker, then tap the terminals from the amplifier on a good speaker. If you hear a small pop it’s because there’s DC there.
If there’s a feature request to be made, it would be to the GStreamer team I think. “When pausing GStreamer, send a digital zero to the output.”
Again, all off the cuff and I may be wildly off-base.