Yes, both players lose is an explicitly stated possibility under the official Japanese rules.
I’m not aware of it ever happening in a professional level game. I imagine that in most casual games, even though it does occasionally happen, the players are unlikely to be aware of this technicality and resolve it some other way.
Both players could still always misunderstand the life and death status of something, like maybe they both think and agree that something is either dead or alive, while it is actually still unsettled. In that case, the game would likely just end with mistaken scoring rather than them ever becoming aware that they should have had a both players lose situation (unless some arbiter steps in to help clarify).
My belief is that the judgement is meant to specifically punish both players. I guess in some tournament scenarios, it would mean that neither player gets points or that they are both eliminated (in elimination formats).