Fabric isn’t perfectly airtight. It also can itself vibrate. The sound is a bit muffled but since it’s just vibrations that’s how it works. The doors also vibrate. Even Windows vibrate and state spying has been done by utilizing a very sensitive laser sensor aimed at the office Windows of important people that detect the minute vibrations and can use that to get audio.
Sound is molecules of air vibrating. Those molecules hitting the door make the door vibrate which in turn makes the air vibrate other side, producing the same sound but muffled because the door material is not good enough to reproduce the exact same sound.
Fabric has gigantic holes compared to the molecules of air (you can easily verify this by getting a blanket between your hand and your mouth and blowing) so they have very limited effect on the path of sound.
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