DH - Re-entering question
 

A pinch-runner comes in for the DH.

I'm assuming the following:

1. There is no more DH for this game for this team.
2. The player that was the DH can re-enter the game.
3. If so, if he comes in for the player that was being DHd for, that's simple.
4. If he comes in and the coach removes a player that is batting, the player that was being DHd for now slides into the removed player's batting slot.

Correct?

Speaking FED, The pinch runner becomes the new DH. The DH position is not terminated unless the defensive player that was being DHed for goes into the offensive side of the game.

Regardless, the starting DH is no longer in the lineup and is allowed to reenter as long as he reenters in the same spot of the batting order.

Since he can re-enter and assuming that the defensive player has not gone into the offensive lineup, the original DH can still be the DH when he re-enters?

Yes. As long as the DH position exists, a sub can come in the game in the position and the starting DH may reenter in the position. The position only ceases to exist if the fielder being hit for comes to bat or the DH enters the field defensively.

Additonally, the starting DH could re-enter the game and play defensively causing the current DH and the player being hit for to be removed.

What about this:

Abe is the DH.
Bill is the defensive player being DHd for.

Abe singles.
Bill comes into PR.
Bill does not bat.

Is the DH still existing if Abe then re-enters for Bill? In other words, does the defensive player have to actually come to the plate in order to kill the DH?

See my post above. Bill the player DHed for, is now playing offense. DH is terminated.

The "playing offense" is what I need clarification on. If the defensive player is a pinch-runner but never comes to bat that inning, is that "playing offense?" Or does he have to come to bat before he is "playing offense?" I'll assume by your post that the fact that he's a PR constitutes "playing offense." Correct?

Yes. Think of it this way: If he's on base, he can possibly score, and the only way to score is if you're on offense (except in football) :)

Running is playing offense. If at any point the player who is being DHed for participates in the offensive half of the inning, the DH is terminated.

Thanks for the clarification.

1) False [assuming the runner is NOT the DH's defensive counterpart]
2) True, as the DH or on offense
3) True
4) False: both the DH and the offensive player counterpart are, like everyone else in the batting order, locked in place in the batting order. Nobody in the batting order can "slide" into a different slot.

But only because the player who was being batted for already occupied that batter slot. If you send the non-batting player to bat, he assumes the DH's batting slot. Indeed, he already occupied it.

From The Rule Book
 

To simplify the thread - I am posting the actual rule from the book

ART. 4... A hitter may be (not mandatory) designated for any one starting player (not just pitchers) and all subsequent substitutes for that player in the game. A starting defensive player cannot be listed as the designated hitter in the starting lineup. A designated hitter for said player shall be selected prior to the start of the game, and his name shall be included on the lineup cards presented to the umpire-in-chief and to the official scorer. Failure to declare a designated hitter prior to the game precludes the use of a designated hitter in that game. If a pinch hitter or pinch runner for the designated hitter is used, that player becomes the new designated hitter. The player who was the designated hitter may re-enter as the designated hitter under the re-entry rule. A designated hitter and the player for whom he is batting are locked into the batting order. No multiple substitutions may be made that will alter the batting rotation. The role of the designated hitter is terminated for the remainder of the game when:

a. the defensive player, or any previous defensive player for whom the designated hitter batted, subsequently bats, pinch-hits or pinch-runs for the designated hitter; orb. the designated hitter or any previous designated hitter assumes a defensive position.

I believe the answer to cshs81 is in bold red.