Doomed State is the state that a Titan is put into, once its base health and shields have been removed. When a Titan is in Doomed State, the health bar is replaced with a striped black and yellow bar, signifying to the player of the Titan's health. External changes will also appear, with the Titan's chassis being shown as charred, on fire and badly damaged. These changes are irreversible (with the exception of the Monarch Titan, whose Survival of the Fittest kit allows Batteries to repair out of Doomed State), and once a Titan has been Doomed, it cannot be un-doomed.
In Titanfall, the health bar will slowly erode over the course of several seconds, meaning the player must eject immediately or die in their inevitable explosion. In Titanfall 2, the Doomed State will not automatically erode, and a smart Pilot can survive in their Doomed state for the entire match if they play smart. However, the new rodeo system means that a Pilot who is succesful at removing a Battery or throwing a Frag Grenade in the exhaust will instantly kill a Doomed State Titan, regardless of how much health the Titan has left.
Additionally, any Titan that is in the Doomed State is in risk of being Terminated. At the launch of Titanfall 2, this risk could be put aside as long as the Titan in question had any amount of shield remaining. However, as of Monarch's Reign, any Titan in the Doomed State can be Terminated, regardless of shield status.
In Titanfall 2's version of Frontier Defense, a special Amped Battery can be purchased between waves to bring a Titan out of the Doomed State. Fully repairing a Titan in this manner is very expensive though (each battery costs 500 credits, and several are necessary to bring a Titan back to full health) and so Pilots may prefer to sacrifice their Titan and redeploy at full health at a later point, especially if they possess a Nuclear Eject system.