What happens to sound waves?

No, It's not possible. Sound ultimately transforms into heat energy. You can not reproduce all the useful and useless sounds from history. In general all energy is ultimately converted to heat energy and heat energy flows from an object at higher temperature to an object at lower temperature in order to attain thermal equilibrium.

Just one more aspect to consider is the comparison with the electromagnetic waves from radio and TV broadcasts. One could ask the analogous question here:"what happens to them?" The answer is that some were broadcast also into space (when transmitters were entirely undirectional) and so are still available for reception, albeit only by aliens light years away and very attenuated.

Sound waves stay on Earth in the atmosphere, and become part of that atmospheric motion, which is gaseous motion. This motion exists because there is a non-zero temperature for the atmosphere (say 300K). So the sound wave attenuation will reduce the given wave intensity, and corresponding particle motion, and corresponding air pressure difference (which is sound) below that of the ambient atmosphere. In a good (outdoor or indoor) auditorium the sound can last for longer and travel further, but eventually it will reach the general level of atmospheric noise.

So I suppose that with sound (unlike with EM waves in space) one could say that the medium ultimately destroys the message.