No One Has Ever Scored a One-Point Safety in NFL History
The point structure should be obvious if you have any general knowledge of how American football operates. Six points are awarded for a touchdown, seven for an extra point kick, or eight if a two-point conversion is successful. You can also score three points by kicking a field goal. The one-point safety is far less well-known.
The idea of a safety is not particularly uncommon. A safety is a tackle that results in a player being stopped in their own end zone, and it awards two points. They occasionally take place. That is, nevertheless, a two-point safety. One-point safeties are extremely uncommon and have never occurred in NFL history.
A lot of extremely bad things need to happen for a one-point safety to happen. After scoring a touchdown, a team must attempt an extra point. Typically, this is run-in for a two-point conversion or kicked for one point. The team attempting to score the extra point would need to somehow make it to their own end zone, nearly 100 yards back down the field, and then get tackled by the opposing team while they are there in order for the one-point safety to occur. Really, there is no logical justification for it to occur, which likely explains why it hasn't.