There are still some regional "
unreserved" trains where you don't buy a ticket for a specific train, just for a route. These can have more riders than seats.
Calling it "unreserved" is somewhat of a misnomer by Amtrak. I'm pretty sure that every prepurchased single-ride ticket has a scheduled train number and date on it where all scheduled passengers will be available on the train's (virtual) passenger manifest whether or not they've boarded. I've also been on the Pacific Surfliner where they were short-staffed and the conductor announced that he was going to bulk lift (an option on the conductor's app) every ticket that was scheduled since he was unlikely to reach ever passenger in time.
It's also possible to just board a train and buy a ticket from the conductor, and theoretically a lot of people can do that. I did that once, where there was no surcharge since there was no ticket sales at the station. At first the conductor was kind of angry at me for wasting his time since it was clear that I had a mobile phone and credit card. But then he loosened up and went into detail about the onboard ticket he was issuing, which looked like an old school train ticket.
Someone willingly posted this to a public website, so I'm not sharing any private information (plus the ticket has long expired). But it certainly has a train number and date. My understanding is that the ticket (if unused) is valid for a single ride up to a year from when the reservation was made.
I don't know if they "overbook" so-called unreserved trains, but there is the option is to use an unused ticket on an earlier or later train than scheduled, so there's the theoretical possibility that a lot of passengers opt to board a particular train beyond its theoretical capacity. There are also multi-ride and monthly passes that don't account for such passenger on specific trains; passengers just show up. Not sure about now, but at least at one time it was possible to get those and use them on certain reserved routes. Also possible to use those multi-ride and monthlies on reserved Pacific Surfliner trains. I think some comments here have been that it can get really crazy when there are a lot of people going to Del Mar Racetrack during the racing season. Supposedly every seat is taken and they rely on using the cafe car.
There are some outliers other than multi-rides and monthlies. I remember when I used to ride the Capitol Corridor a lot and there was the option to use an unused unreserved ticket on the San Joaquins for any overlapping city pair, like EMY-MTZ. I'd think that's not likely to happen much. I did it once just to see if it worked. The conductor said it was OK and my ride was credited with points to my AGR account.
I looked it up, and apparently anyone with a multi-ride or monthly pass who wants to use it on a reserved train will need to make a confirmation for that train to apply the the pass. I suppose that's different than the old process of just getting on and having the conductors deal with the possibility of a full train.
Passengers traveling with a Multi-Ride Pass (monthly, ten-ride or six-ride) on reserved services, a USA Rail Pass on reserved and unreserved services or with a regional rail ticket on reserved services where travel on specified Amtrak trains is permitted and requires ride confirmations will need to confirm their intended trip prior to boarding. This allows us to ensure a seat onboard for each passenger and to account for every passenger traveling; thus ensuring you have the safest and most comfortable journey possible.