I've been the player with <10 Con. (a 6 con 6 str Xeph Ardent blaster/constructor). I spent a lot of power points on Vigor (from Expanded Knowledge) throughout the day, and liked to stack Haste from a party member with my own Xeph Speed Burst to make SURE nothing ever got in melee range of me. Made a fun challenge.
The Duskblade in the same party had a Con near 30, and Diehard.
I can't think of anyone else who has run a low-con character though.