When you take damage with AbsorptionAmount set to NaN, you get stuck in the dying animation and become invulnerable. While in this state, you can't take damage or die, including via /kill. You also cannot pick up items.

Steps to reproduce:

• Create a vanilla server, log in at least once, then log out.
• Open the playerdata file with an external NBT editor
• Set AbsorptionAmount to NaN and save
• Log back in and take damage (or /kill)

The only way I've found to fix this is by resetting AbsorptionAmount to 0 with an external NBT editor

Note: This never occurs in Singleplayer, as AbsorptionAmount is reverted to 0

(I'm not sure how this happened the first time; I was using bukkit though)