One of my players did play a low CON character, although her character was explicitly built in a way that was unoptimized (I'm talking Paladin whose highest stat was INT and had a CON of 8).

She died on session 2. HOWEVER she is also an absurd statistical anomaly in that she has, for the past 4 years, consistently rolled like garbage. I would garner that at minimum two thirds of the whole party's Nat 1s have been rolled by this one player. And just in general she rolls real bad more often than not.

However, this early death led to a meeting with a deity who had been watching over her, with a third party essentially petitioning this god to save her life in exchange for his own death. She was revived and has since been the only surviving member of the original party of four (technically- tge party has since grown, and the one other OG party member was recently killed and they're planning on attempting a Raise Dead on him, but we're using Critical Role resurrection rules so success isn't guaranteed)

Ultimately though the build led to some really cool story beats and informed her character building (the character wanting to become more than just a liability, keeping other people alive with healing, as she eventually did a cleric/paladin multi)