Dead Ball Foul or Not
 

Team A in punt formation. 10 Guys on the field only 6 on line of scrimmage.
11th guy is trying to run on field as ball is snapped but doesn't get on right side of ball. Do you blow it dead and stop the play immediately or do you let the play run and then call for illegal shift(motion).

It is a live ball foul, a sub is not a player until he is on his side of the Los so he is not offsides. He is however still a sub who did not complete a substitution, so it will be an illegal substitution, but if he participates in any way then it is the more serious illegal participation.

You also have a live ball foul for an illegal formation.

The substitution and formation foul occur at the snap and if either is accepted would be enforced from the previous spot. If it becomes IP then it happens when and where he participates which may matter for enforcement.

By "right side of the ball", do you mean he's on the defensive side of the line when the ball is snapped? (If so ... why "illegal shift"?)

By "right side of the ball", do you mean he's on the right but supposed to be on the left and is in motion when the ball is snapped? If so ... is he the only player in motion? How many are actually on the line when the ball was snapped?

I mean he is on the defensive side of the ball and is running to the offensive side (punt team''s side)

Got it.

Then what Rev said. :) Most likely IP unless he doesn't affect the play in any way (usually this means he ran right back off, or possibly no one reacted to him at all, and the kick was not returned).