DJstormtrooper42 asks:
Two questions:

1st
From the rulebook:
"During your turn, effects from your opponent’s cards may not include or consider your stopped personnel."

If this is the case, how does a card like A Bad End or Don't Let It End This Way legally function?

2nd
"You cannot use another card’s text to affect one of your stopped personnel or ships."

If this is the case, can a affected by Brief Reunion be killed while stopped?
For your first question, the golden rule of CCGs is that cards may break a rule if they explicitly do so. A Bad End and Don't Let It End This Way explicitly break the rule about whom dilemmas can affect.

For your second question, yes, a personnel placed in play by Brief Reunion will still be killed at the end of the turn even if that personnel is stopped. The reason is the same as why Michael Eddington will still be killed if his ability is used and he is stopped: you activated the game text before the personnel in question was stopped. An effect that is already pending on a personnel or ship is not cancelled just because that personnel has been stopped.