Hi Brian.
Well you have different choices to make that work. You can have a global stateful session where all your processes will leave. If you are using persistence you don't need to worry about your processes, because each time that you interact with them the change of state will be persisted inside the database. If your server goes down, you only need to recreate the session and register all the workItemhandlers, globals and the human task handler (special type of workitem) in order to your process continue working.
About the objects inside the statefulsession it's the same.. Instead of recreating the session you can store somewhere the session id and when your server restart, you can query the database in order to get the latest snapshot of the session. In this situation you must register all the handlers again too.
Hope it helps!
Greetings!