Purchasing tickets for late trains

[Anderson]

Is there a way to purchase a ticket for a late train after that train is supposed to arrive at a given station? I ask because there are some trains that are a bit infamous for running very late and/or where a late train would in effect offer rare mileage (i.e. the SWC doing Cajon Pass in daylight or the Coast Starlight running down the CA coast at night/heading through the mountains during the day). So if one finds out "Hey, train X is way behind schedule and it's going to let me do unusual run X", would it be possible to snag a ticket after the "on paper" departure time but before the train actually arrives?

 

[bobnabq]

My answer is "I don't know" but I'm going to guess if there's an agent there he/she may be able to sell you one.

Now, we await a more informed response.