Instead of the standard 10 negative HPs, you can rule that your negative HPs equal your Constitution score. In this system, you don’t die until you reach a number of negative HPs equal to your Constitution. You can now potentially lie on the ground “dying” for a lot longer, which means your team mates don’t have to run and save you right away.
This rule changes Phoenix a lot considering that it’s possible to pump your Constitution up into the 20s or 30s using Ability Boost and Ability Enhancement. It creates a situation in which those who have high Constitution scores and take the Dieheard feat are nigh unkillable. The corollary is that high Constitution scores become far more valuable.