In the case, say the EB is running maybe 3 hours late, I assume they will not hold the Cardinal? What would be the chances of them busing us ahead to catch up with the Cardinal? I think putting us on the CL would be rediculous and pretty much ruin a trip after already having bought rooms and would be forced to coach. Vouchers would be usless as well since I only hit the rails once every few years as a treat.
Holding the train is done on a case by case basis. Generally they wouldn't hold the Cardinal for you if you are going to the East Coast - they would put you on the CL or the LSL if you make it in tme. If you can't make the LSL, you will overnight in Chicago in a hotel room on amtrak's dime.
You are always at risk of a forcable downgrade to coach if you miss your original connection.
When I was on a very, very late eastbound EB in July 2012, I had a planned overnight in CHI and was booked on the next day's LSL. There were lots of people in my sleeper that had missed connections. One of them got downgraded from a bedroom to a roomette on our train, but I saw another guy in coach (not sure if he just didn't push for the roomette or what). There ended up being empty roomettes in my car, but the train the day behind us was late as well and also misconnected to the LSL. So I am sure some folks had rooms on the LSL from that day's EB that were then freed up for folks on my train.