Third rails generally carry 600 volts or 750 volts, although each city's system is different, and the voltage may vary. They're powered at all times, since they span the entire rail system that always has trains on it.
These voltages aren't generally strong enough to kill, just severely injure. To kill, you need at least 1000 volts. The guy you were talking about probably wasn't killed by the third rail alone. He may had a concussion and/or damaged his spine from the fall, while also getting electrocuted.
Also, the third rail is much deadlier on grade-level lines than on elevated lines. Reason being that on elevated lines, you have to touch the third rail and the main two rails for it to shock you; it'll do nothing otherwise, like birds sitting on power lines. While on grade-level lines, if you touch the third rail and literally anything else, you'll get shocked very hard, just usually not enough to kill. Subways are the same as grade level, as the conductive concrete the tracks are laid on touches the Earth's soil.
"How do you know this?", someone might ask. I'm a railfan. I like trains, their history, and learning how they work.