A one-point safety can be scored on an extra point attempt if the team on defense obtains possession of the ball as a result of a turnover such as a blocked kick, interception, or fumble and retreats back or laterals the ball back into the end zone followed by the player possessing the ball either being tackled down, downing the ball, or fumbling the ball out of the back of the end zone. Another very extreme way to score a one-point safety would be if an offensive player was sacked in their own end zone on an extra point which is 98 yards away, but that type has never occurred.
I just coincidentally looked up the one-point safety rule last week since an article from CFU was referenced by the blog called The One-Point Safety. The author of the blog, Travis Normand, witnessed live the one-point safety in the 2004 Texas vs. Texas A&M game. Once seeing it last night, I was shocked more, not by the surprise of the rule, but by it actually happening after I recently looked it up. It is the most rare way to score in football.
Watch around the 3:00 minute mark of the video below for the one-point safety in the Fiesta Bowl. Oregon's extra point kick was blocked and the ball was carried back in the end zone by a Kansas State defender.
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Known One-Point Safeties
1. Westminster vs. West Liberty State (NAIA Division II), September 7, 1996.
2. Moorpark College vs. Bakersfield (Junior College), September 21, 1996.
3. Texas vs. Texas A&M, November 26, 2004.
4. Oregon vs. Kansas State (Fiesta Bowl), January 3, 2013
Source: Quirky Research