It varies by the train and the circumstances. It is NOT a guarantee that the outbound train will be held, only that Amtrak will get you to the destination.

Since the Sunset only runs 3 times if the Starlight is only a little late, chances are they might hold it, but only a little late (probably <30 minute delay to the Sunset). Otherwise the most common solution is to take you off the Starlight up the line at Santa Barbara or Oxnard and bus you to catch the Sunset at Palm Springs. If the Starlight is already really late by the time you get into Sacramento and the Bay Area, they'll likely take you off the Starlight at Sacramento, Martinez, or Emeryville and put the Sunset passengers on the San Joaquin train/bus connection to LA, which is much faster than the Starlight.