If K recovers the ball behind their line of scrimmage, they can do anything legal that they want to it - run, pass, or kick it again.
If R touchs the legally kicked ball beyond the LOS, K picks it up behind the LOS, and then K throws an incomplete pass, do we have 1/10 for K, or for R?
These two Case Book should provide answers ...
5.1.3 SITUATION C: Fourth and 10 on K’s 45-yard line. K1 punts the ball beyond the neutral zone. R1 muffs the ball back behind the neutral zone where K1 recovers and: (a) falls on the ball at K’s 40-yard line; or (b) throws a forward pass to K3 which is complete at the 50-yard line and R1 interferes with K3; or (c) K1 punts the ball and R1 fair catches at his 30-yard line. RULING: Since R1 touched the kick beyond the neutral zone, it will be first down for the team in possession in (a), (b) and (c). In (a), it is a first down for K at K’s 40-yard line. In (b), the pass is legal as there had been no change of team possession. If K accepts the penalty for interference, it will be K’s ball at R’s 40-yard line. In (c), the second punt is legal as there had been no change of team possession. The ball belongs to R first and 10 on its own 30-yard line. (5-1-2f; 6-2-1; 7-5-1)
*5.1.3 SITUATION D: K’s ball, fourth and 2 at midfield. The scrimmage kick crosses the expanded neutral zone and is muffed by R at the R 40-yard line. The ball then bounds back behind the line of scrimmage and is recovered by K2 at K’s 43-yard line. K2 advances to K’s 49-yard line where he throws an incomplete pass to eligible receiver K80 at the R38. RULING: This is not an illegal forward pass as the ball was legally thrown behind the neutral zone. There has been no change of possession during the down. K is awarded a new series as the ball was touched by R beyond the expanded neutral zone and K is in possession at the end of the down. It will be K’s ball, first and 10 at midfield due to the incomplete pass. (7-52; 2-34-3; 5-1-3f; 7-5-5)