Yes. You will see this happen when the punt is headed very close to the returner's end zone. Instead of the punt returner catching it and giving his team poor field position, like at the 5 or 10 yard line, he will usually let the punt hit the ground in the hopes that the ball will bounce into the end zone so a touchback will be called. In this case the ball would be brought out to the 20 yard line and the returner's team would go on offense. But if the punt team can get down fast enough, they are allowed to catch the ball as long as they do not interfere with the returner.
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If you are a K player (kicking team) and 'hit' or 'make contact' with the R player (receiving team) trying to catch the ball before or during the catch, it is a kick-catch interference foul. The R player attempting to catch the kick is given protection. He is given an 'opportunity to catch the ball'.
If the R player asks for a fair catch, he is never to be hit, unless the ball hits the ground.
The play stops where the player caught the ball, and the other team starts from there.