Something came up in my sorting for Shang-Chi and the Legend of the Ten Rings that I thought I should separate out in case people aren't interested in that post or are avoiding spoilers. (If you like the MCU and can watch safely, I highly recommend it!)
One of the characters had a Burnt Secondary, but wasn't fully burnt. In fact, only the Multiplayer part of the secondary was burnt; the Single-Player part was perfectly healthy. Now that we've begun talking about Multiplayer versus Single-Player, I think it's not too much of a stretch to say that only burning one part makes sense as a possibility. I've rambled some about how I'm a Snake secondary who uses Courtier Badger instead of a mask. I didn't feel right calling my Snake burnt because I was still using it in Single-Player situations. I joked that I follow PvP rules but not PvE. But if it's possible for one side to burn while the other stays relatively healthy or for one half to heal from a burning while the other half stays burnt, it makes a lot more sense for me to say my Multiplayer Snake is burnt while my Single-Player Snake isn't and that I built a Courtier Badger model to handle social situations.
Obviously, the Single-Player and Multiplayer parts of the secondary are connected. A vast majority of the time I would expect them to burn together or that one side burning will lead to the other burning too. But I think making the distinction that they can burn and heal separately is an important possibility to explore.