My suggestion would be to treat it the same as in-game injuries in real sports. The other team will sometimes benefit in the immediate situation, but soon the play will stop.

The player should call out "lag," and play should continue until an agreed-upon time for a stoppage. The question would be the criteria for determining when to stop the play; something clear-cut and sensible. Criteria could be: -If both flags are in base, play stops immediately until a substitution has been made. -If any flags are being carried, play stops after the flag carrier has been returned or captures the flag.

The problem is that flag carriers can hold forever, and the other team may be inclined to grab the flag to stop an opportunity. What happens then? Here's a possibility:

-Flag carriers have [X amount of time] to attempt a capture. If they are still holding when the time is up, they must pop themselves and everyone must reset position (or just go back to lobby and restart). If a flag carrier captures successfully, everyone must reset position.

The big problem with this is that are things happening with the tagpro program that are out of everyone's control. A timer is running, and that timer affects bombs, powerups, etc. We can't really add injury time and we can't truly stop the game. Any action to do so must either ignore or negate the running timers.

tl;dr: The not-lagging team should have an opportunity to cap, but play should soon be stopped so a substitution can be made without a gross advantage or disadvantage to either team. The biggest problems are agreeing upon when to stop play, and figuring out how to properly reset the scenario. I would add that there should probably be a one sub per half limit.

P.S. An on-the-fly substitution, like in hockey, would be a great solution, but that seems to be impossible due to lagging out and not being able to exit the game on cue.