If the Starlight is running Late and Amtrak has determined that the connection with the SunsetLtd./ Texas Eagle will be missed, you would probably be de-trained in Sacramento or Martinez and be put on a San Joaquin Train/ Bus ( change in Bakersfield) to LAX.

This is a guaranteed connection so Amtrak will get you to Chicago ASAP but you won't be doing a layover in LA to catch the next Sunset, it only runs 3 times a week.

Don't worry, enjoy the nice ride and scenery and leave the "driving" to Amtrak.