I've played it out a few different ways over the years. We've talked about that a bit up thread, but here is a case I have in mind.
The PCs are taken captive in what would otherwise have been a TPK (as often advised in official published material.) The NPCs want to pry crucial information from them, which the whole party have promised one another to withhold. We're not interested in torture-porn so we have no interest in narrating the process in any detail. Each player is now put in an awkward position? What decides if their character spills or not? In the end, the players found it to be a relief that I let the dice decide. It made perfect sense to them that they might have been able to say nothing, but there was a chance they would break. It avoided any player having to intentionally do something that might have felt at odds with their commitment to the party.
This certainly isn't the only way to run the situation, yet unless the situation is something a group are anxious to narrate, it is a decent way to do it. I wouldn't mind a DM saying - yes C you hold out as long as you can and - make a roll - you give up the location of the prince on the 3rd day. If a DM asked me if I caved, I think I'd prefer to roll, in most cases.