Server/Client relationship in Single player

I’m curious in Multplayer the server is “always” up so stuff happens when you aren’t playing (thrall production and the such) When you are away though you are not losing water and food and don’t have to feed yourself etc.

Is there anyway in single player to basically exit the character but leave the server side running in the background in a similar way?

No, you will need to set up a dedicated server for that. I do know some have machines powerful enough to handle the client with a dedicated server set up on the same machine. They have done that. I have not.