If the collapsed lung is not treated at a hospital then yes the collapsed lung can become life threatening.
If you suddenly get a collapsed lung you do need immediate medical treatment if you want to live.
When your lung collapses you'll struggle to breath and lose oxygen to your brain and when you can't get enough oxygen you die.
This is what sometimes happens to people is car accidents where they die.
They sustain damage to their lungs and the lung collapses causing them to die due to difficulty breathing and loss of oxygen.