A large part of the US depends on septic systems. After flushing, the water, feces, and toilet paper all end up in a tank on the property. The toilet paper and feces there dissolve into the water thanks to bacterial action and other processes, and then eventually flows into a field line that distributes the water into the soil. This is entirely a passive process that can go decades without maintenance, though newer designs in wetter areas sometimes have a pump that sprays the water on the surface after chlorinating it.
https://en.wikipedia.org/wiki/Septic_tank