I don't think the fire is mysteriously gone in this imagining of the analogy. More like it is still there, but is survivable: still very hot, still very scary, but not clearly moving to inevitably consume you. I think this is just another place where the analogy breaks down. But that's ok, no analogy is perfect, but I think this one does have its uses.
I still think the original analogy works here - if you make sure that in the moment of panic the windows don't open to prevent voluntary and quick death, the person now has to suffer the agonizing pain of the flames for the rest of their life.
It holds even more true if we consider that a large part of suicides are not because someone wants to die - no - it's because someone does not want to live like in present situation anymore. Just like with the fire, the goal is not to die on a sidewalk - it's not dying in the fire. You attempt suicide as last resort - if you die, it's okay, it's final. If you don't, it perhaps changes something for the better.