Can I Get a Refund If the Train Does not Show Up?
Unfortunately, almost all city trains and buses do not refund any fare products. Look up the train company's website to see if they offer Delay Repay (they might call it 'delay compensation'. In that case, you are legally entitled to compensation of: probably up to 50% of your ticket price if you get to your destination between 30 minutes and an hour late, a full refund if you arrive more than 1 hour late.
You should check every company's refund policies. For instance, an unplanned disruption, like the roughly hour long shut down of the Blue and Yellow lines (DC) Monday morning, would qualify for a refund as long as riders have registered their SmarTrip cards with Metro and tap out of a destination station more than 15 minutes later than the longest expected trip at that time of day.
Airlines too have their refund policies listed on their websites. Most of these however, also state that they are not responsible for delays beyond their control such as acts of nature.