There is not a scenario you can cite here that will cause someone to give the same definitive course of action to take each time it happens. Of course there is a type of scenario you can bring up in which you should virtually always respond with action - the scenario is that the bad guys have started killing or are obviously about to kill. In that scenario it is time to act with deadly force if you are a law enforcement officer. Sadly this does not always take place. Law enforcement officers have been known to hide their creds and guns in such situations hoping to be left alive, but once the killing begins or is imminent it is time to act.
As far as escape goes, and LEO taken hostage with other hostages has a tough choice to make about escape if it is likely he/she will be the lone person to get out. The LEO may decide that he has seen enough to give extremely valuable intelligence to other officers who are on the outside, or the officer may decide that he or she has an obligation to remain inside and try to prevent any killing as best possible.
If you suddenly found yourself in a scenario like the diner scene in the movie Pulp Fiction, what would you do? There is a scenario that is quite possible, and in fact has taken place. As an armed person or LEO you may decide to immediately try to take out the two assailants; but what if there was six of them. What would you do. Now make that a bit more complex. The six assailants who are all armed with firearms, start robbing the people and making them empty pockets then stand up for a quick pat to see if they withheld anything. You are at your table far away in the corner. You are armed and you are a credentialed LEO. What do you do?
To make it worse, you are sitting their with two other officers, who just hid their credentials and their guns in the crack between the seat and seat back in the booth in which you are seated. What do you do?
Or even worse, you are seated there, with your spouse, your daughter and your son; what do you do? What would you do if your 5 year old son suddenly blurts out, hey dad why aren't you arresting them? Are you ready for this type of a situation when all the attention has just focussed on you? (Hopefully you have trained the family to keep quiet and hit the deck if you give the signal.)
Many LEOs refuse to carry off duty because scenes like this can come up and they think themselves and their families better off if they are not armed. I on the other hand believe it better to be armed, and to take action if necessary. I feel this way because if I am unarmed I am totally at the mercy of some dirt bags who may decide that mercy is not something they are doling out today, or who may simply be intent on killing a fat, middle aged guy like me. Of course, I may act, and my actions may be the wrong ones that lead to someone getting hurt or killed. While it would be very difficult to live with I think I could someday comes to terms with the actions I took or even with my decision to take action. I do not think I could live with myself if I did not act and someone was killed or hurt because of my inaction especially when I had planned that inaction in advance of the event even occurring. Bear in mind that inaction on the part of several hundred people helped contribute (not cause or be responsible for but contribute) to the success of the 9/11 hijackers; just as the actions of those on the flight over PA undoubtedly led to the failure of the hijackers on that plane. Their action also quite possibly led to the saving of hundreds if not thousands of other lives, and maybe even to saving of our nation. Those hijackers had banked on compliance, on the herd factor so to speak; they did not figure the herd would strike back though on that one flight as most herd animals are not like water buffalo or elephants - most are like sheep. As soon as the hijackers realized it they put the flight down to earth. Yeah they killed everyone aboard, but their mission a failure thanks to those on that flight who took action in the face of doom. Imagine them having hit the White House and killing hundreds therein!
Who knows what other countries may have done had the White House been destroyed along with the lives of our president, vice president, and other high officials. Remember that the Pentagon had been hit too as had the trade centers. Maybe some countries or other groups of terrorists would have seen that as a sure sign to give us hell. Surely those whimps in Europe would have just pissed their pants if someone else said hey let's send the good old USA a nuke or two. Who knows how we would have reacted, maybe we would have sent out a few ourselves. Another big what if would have been had they actually hijacked the amount of planes they had first planned to hijack. I think the number was about 15. Would the people on later hijacked flights reacted like those over New York and Washington, or would they have been like those over PA?
My point is that is you are in a situation that is resulting in death or which is likely to result in death, then you have an obligation if to no one but your own conscience to act to prevent it. Even if you are certain it means your own death, you have an obligation to prevent the death of thousands of others if it is at all possible. When it is do or die or even do and die, I hope to choose the do part when it means saving so many other lives, and who knows maybe I will crawl out of the carnage with my enemies lying dead around me.
This is all talk on my part, but it is what I keep telling myself, and what I keep volunteering for in my job. No I do not have a death wish. I want to retie when I can. Then I want to live so long that the government will send investigators to see if is really me collecting my pension; but if I have to do the right thing when the SHTF then I hope I have prepared myself well enough to actually do it.
I gotta stop now, because the more I think of this kind of thing the more scared I become. It is not a nice feeling at all to think about such things when the results could be as final as they could be. I have prepared, I have trained, hopefully it has been enough if it ever happens when I am there.