rjack321:
If you know you have enough to exit, like it was a small scale reg failure, sure stay on your own long hose. But if the right tank may be significantly depleted and run out mid-exit - then share gas prophylacticly within the team to avoid an obligatory share.
I'll address this from a cave diving standpoint, since that is what I know best.
In theory, if someone has to isolate their tanks, then there should be enough gas in the remaining tank to get that diver out of the system without having to share gas. However, there may have been some gas lost dealing with the incident, and if it was the left post that had to be shut down, then you have no idea how much gas actually remains. So there is at least some chance that the diver will run OOA before you reach your stage or deco bottles.
In terms of "what to do", it is definitely easier and quicker for two divers to travel while breathing from their own back gas, so that might seem like the way to go. However, you always have to keep in mind that the diver with isolated manifold might run out of gas without warning, and at any time during the exit. So the biggest potential risk in this scenario is having a diver run OOA in a situation where you cannot get gas to him immediately - for example, swimming through a single file restriction or a tight passage where there is limited room to maneuver without destroying the viz.
It's probably OK to have the afflicted diver breathe his own back gas when you are traveling through large passages where you have more room to manuever. Any time you enter a tight area however, you need to make sure he is sharing gas with someone. This allows you to take advantage of the gas in the accessible tank (which seems prudent in this situation), while mitigating the chances that the diver will run OOA in a tight spot.
And of course, the decision of when/whether to do that needs to be made based on the particulars of the dive, the team, and the state of mind of the person who is OOA. That's where the "thinking diver" thing comes into play.
FYI, this is one of the reasons why DIR gas management procedures dictates preserving a little more gas in the doubles than in the stages - it gives you just that much more of a cushion in situations like this.