Chicago is a very popular, busy City so it depends on the time of year and the scheduled activities going on in the windy City as to available Hotels!
There is no hard and fast policies @_Amtrak for missed connections except for the late Thruway bus to Michigan that has been added. Makes no difference as to Sleeper or Coach, its first come, first served @ Customer Service, but Sleeping Car passengers get first crack @ Sleepers on rebookings on alternate trains!
I've stayed in Hotels and Motels that ranged from the downtown 4 Star Hyatt to suburban Motels, but always received money for taxis ( if in Chicago, otherwise vans or a charter bus wee used for groups) and meal money!
The biggest concern involves the availability of Sleepers on the next days train ( or in the case of the Cardinal the day after train), rebooking are first come first served by Customer Service. You may end up on Coach if the LD Trains are Sold out, or be booked on alternate train, ie Cap Ltd. or Lake Shore/ Regional etc.
In the case of cancelled trains with no alternate transportation on non guaranteed connections, full refunds are offered, but you're in your own to get to your destination!
I've actually been rebooked on a plane a couple of times out of Chicago, but that seems to be rare now a days.
As the old saying goes, "you pays your money and you takes your chances" but Amtrak will get you there on guaranteed connections, eventually and somehow!