[x0x0]

Here's the thing. Your writing doesn't make it sound at all like this person trusts you, and you said you're doing this in a quasi-official capacity.

Those two things make me think your management either sucks, or fucked up and wants to know what your coworker will say.

If you had a good relationship w/ this person already, you could take them out to coffee and pretty much ask, "so, what happened?". Since you don't, and since your coworker is presumably not stupid, you're probably going to get the same answer that your management team would get.

Which brings me to my next point: your management team should know. If this person's boss isn't doing weekly 1-1s and closely monitoring this person's enthusiasm for the job and company, then they're an incompetent boss. That's table stakes for competent management.

Particularly when a coworker quits over an "I'm not a good fit", that means (1) there's a problem, and (2) I don't trust management. Acting as an agent of management isn't going to get the answer.

[cbanek]

Totally agree with this, and I'll take it one step further - if they trusted you and were on friendly terms, they probably would have already told you or asked you for help on what is going wrong, long before they quit.

[itronitron]

The leaving coworker can still be friendly and trust their colleagues but may not share details so as not to ruin their colleagues' perception of their employer.