When you are out of health points, Quick Thinking uses your residual energy pool as an additional health buffer.
When Quick Thinking is equipped, your energy inherits the current armor of the warframe. The efficiency value will act as an additional damage reduction with the values listed below.
As of Update 11.1.0, Quick Thinking will keep your minimum health at exactly 2 HP and use your remaining energy to keep you alive from incoming damage. The efficiency will go up with the mod's level.
Rage will still grant you energy taken to your health until you reach 2 hp (filling up your energy pool), at which point the mod will stop giving energy (as you are not taking health damage) and Quick Thinking will take over, using your Energy pool as a buffer against your remaining 2 hp. Once losing energy, you will go beyond the 2 hp and die.