That cannot happen. In fact the entire reason that there is trains 21 & 421, as well as similar situations with the Builder and the LSL, is that ARROW cannot deal with passengers properly when the train splits/combines if they don't use seperate numbers. If the cars that run through to LA were called train #21, instead of #421, then ARROW would sell any passenger any seat or room on the entire train to LA, even though the entire train doesn't go to LA.#21 and #421 pax are put in the same sleeper.
But if Amtrak tells ARROW that a car is for train #21, then ARROW will not sell any destination west of SAS in that car. You must have a ticket for train #421 to board that through car to LA. Now ARROW would still sell someone a ticket in that car for train #421 from say Chicago to Texarkanna, if they're willing to pay the premium, but that ticket will read train #421 and not train #21.