You damage your current or (most recent) Cover
Compromises and Going Loud damage your current cover. An example is given in the discussion of Agencies:
Many Agencies refer to such down-on-their- luck Pactbound as “burn Covers,” because they serve the same purpose for their Agents as a prepaid cellphone does for a criminal who doesn’t want the police to easily trace him. The Agent uses up these Pactbound to create an identity she intends to wear just long enough to put on one flashy demonstration of demonic power or to commit a single crime she doesn’t want associated with her primary identity. Once the burn Cover serves its purpose, the demon jettisons it to erase all evidence. (DtD, p.57)
The implication is that the Cover loss goes to the Cover you were using at the time or most recently if the loss occurs while in demon form. Otherwise you couldn't have a burn-Cover.
I think of Covers as costumes in your metaphysical closet. If you stress them too much, they tear and fall apart. You're now naked. But it doesn't affect the other clothes in the closet. A burn-Cover can take all the damage, potentially going all the way to zero. You can now pull another costume out of the closet.
But didn't you just get away cheaply?
One might think of this as getting off free. Have a burn-Cover and then do whatever the Hell you want! Your "good" cover is safe, and your burn-Cover takes all the Compromise.
Well, you are now in Demon form, at zero cover. (If you have multiple Covers, your Cover rating is the value of whatever Cover you are currently using. The Cover you are currently using is now zero, until you put on another "costume.") This is not a good thing.
- Your Supernatural Resistance is now your Primum (usually lower than your Cover).
- You are a very loud blip on the God-Machine's radar.
- You will have to be very careful when switching to another Cover. You are a biomechanical monstrosity. You'll have to hide, put on your "other" costume, and hope that you don't damage it in the process. If the GM knows a demon went in a building and three people come out, those three will have the Flagged condition as pretty suspicious. And you better hope that neither of the two humans saw you change, since that would cause a Compromise roll for your new form.
- Glitches: Failure in a Cover roll can result in a glitch. Dramatic failure can result in a permanent glitch. And glitches infect all of your Covers.
So even burn-Covers carry a risk, even if you have another, strong Cover.