depends whether intent is a required factor for the state's wrongful death statute (my state says it's not, as wrongful death is there for criminal homicides that don't fit the murder statute). if openai acted intentionally, recklessly, or negligently in this they're at least partially liable. if they flagged him, it seems either intentional or reckless to me. if they didn't, it's negligent.
however, if the deceased used some kind of prompt injection (i don't know the right terms, this isn't my field) to bypass gpt's ethical restrictions, and if understanding how to bypass gpt's ethical restrictions is in fact esoteric, only then would i find openai was not at least negligent.
as i myself have gotten gpt to do something it's restricted from doing, and i haven't worked in IT since the 90s, i'm led to a single conclusion.