If you are an early-stage VC, you always back the CEO. Or at least, almost always.
For an early-stage investor, a co-founder break-up is on the Top 5 Dramas. It happens all the time, unfortunately. You try to avoid it. But it’s too common to not plan for.
You can’t fix this as an investor. You can try to bring in a mediator (do this — it does help). You can try to get them to work out their issues (sometimes, if it’s not really a break-up, just drama, this can work).
But after you try to help a bit, you have to just move on. The CEO usually is 50%-90% of an early-stage VC’s bet. You try to be supportive, and if possible, help recruit a VP or two to replace the departing founder. But unless the CEO did something unethical, or is a creep, or the other founder is stepping up as the new CEO (this can happen) … outside of those scenarios, the VCs basically have to back the CEO in this scenario.
At an equity level, ideally, vesting deals with the situation. Sometimes, it doesn’t, and the departing co-founder owns “too much”. There isn’t much to be done.
Now, later-stage investors have a lot more options. They often have COOs and even interim CEOs they can bring in to “help” their investments. They often can be more actively involved.