When it becomes obvious you are going to miss the train, your reservation will automatically be re-made for the next train out or, if it's possible, a bus and/or train alternate connection to catch the train you are reserved on. If the new connection involves an overnight stay, Amtrak will take care of you. You will be instructed where to go in your connecting station to claim your meal and hotel vouchers. If your original ticket arrived by email, the ticket for your new connection will arrive the same way (awkward if you have no way to check email on the train -- when it happened to me on a very late EB, I had to borrow someone's smartphone to know what my new connection was supposed to be). If you do not like the new connection you have been given, you need to call AGR to negotiate any changes to the new itinerary.