I think your question can be rephrased as How do I not die to a dragon. If you solve that problem, you will also solve the problem of dying with the finisher animation. Unless you are okay with dying as long as the killcam is not triggered. I doubt it somehow.
There are basically two ways of approaching this problem of dying. You either need to kill your enemy quicker or you need to die slower. You kill quicker by doing more damage quicker. You die slower by having more health and armor and having appropriate resistance.
A Dragon does 37 damage per attack and a Blood Dragon does 75 damage attack. If you are fighting a Blood Dragon, and your armor is less than 275, then you will die from one bite when your remaining health is 50.
You die when enemy inflicts more damage than your remaining health. Some people believe that when killcam is triggered, the calculation is wrong. That they do not deserve to die from one attack when they have more than 100 health remaining. I have seen multiple posts that complain about the so called "bugged killcam" kill. But I have not seen anyone provide any evidence for this. And I have not seen this in my own play. When I die during a fight, I have found it to be generally reasonable.
It seems that for some people, the belief that "armor is ignored when killcam is triggered" is persistent. Fortunately, it is possible to test this urban myth.
In my case, I have a level 62 warrior character with 520 health with 35% intrinsic magic resistance. The character has a set of Steel Plate Armor that takes me above armor cap to 602, and gives me 37% fire resistance. For the purpose of the experiment, I set the difficult setting to Master, which means the you take twice as much damage from an attack compared to the default Adept level.
I have selected melee type Dremora Valkynaz (16ff8) to be my opponent. Dremora Valkynaz is a level 46 Dremora that comes with a random fire enchanted weapon that can range from Iron Sword to Daedric Warhammer. You can summon it by using console command player.placeatme 16ff8
Highest Damage I observed when not wearing any armor was 413 from a Ebony Warhammer power hit. With armor, highest damage measured was around 100.
I repeatedly summoned Dremora Valkynaz and died to it 100 times wearing max armor while looking for this killcam death that's supposed occur while you have high health.
If the "armor is ignored when killcam is triggered" assertion is true, it would have been possible to observe a killcam death when my health level was below the damage taken when not wearing armor. But no such occurrence was observed.
However, twice out of 100 trials, I observed killcam death occurring when the character had health above maximum damage the opponent can inflict with single power attack. It can happen when you are attacked and then killcam triggers right after that. So if this does happen and not my mistake in observing, characters are vulnerable to insta-death when their health falls below the damage that can be done in 2 power attacks.