If I ever said that it was in informal speech. A rail is a power supply voltage. +15v and -15v for op amps for example. Or +/-50v for a solid state power amp. I think I tend to just say B+ instead of B+ rail, but that would be OK too. But I think of it mainly as a solid state term. But in general it is easier to write "rail" than "power supply" when you are busy.
Stuck means stuck, as in not moving. A relay or an LED is stuck on, my amp is stuck in the clean channel. A voltage signal that controls something - an LDR for example - can get stuck, meaning the circuit can no longer turn it off and on. The term doesn;t specify WHY.
If transistors fail or something the output of a solid state amp can swing over to the DC voltage of one of its power rails - you get a steady 50vDC on the output. I might refer to that as stuck to the rail. Same thing with an op amp. If the IC is bad OR if the input to it is bad, the output can wind up stuck to the 15v rail.
Can you point to a specific example or two? I could then better explain what it meant in that context, perhaps the language was too imprecise.