The three risks that are relevant here are the risk of fire, suffocation and carbon monoxide poisoning
I'll take suffocation first. A gas leak can exclude oxygen to the point that you can no longer breathe, but there are standard mitigations:
- the gas canister is usually mounted external to the passenger cabin, in a compartment vented downwards, so that gas escaping a badly fitted connector will not enter the cabin.
- cookers typically have a safety cutoff that is heat operated, so if a flame blows out, the gas flow will stop.
- propane has a distinctive smell added, so it may wake you.
- while the main leak risk is from the connection to the canister, there is obviously a risk of leaks anywhere, so gas leak alarms are used
Carbon monoxide poisoning is unfortunately a bit more likely. Carbon monoxide is typically a byproduct of burning a flame without enough oxygen, so the usual mitigation is to have a window open. Simple but effective. Like the propane detectors, carbon monoxide detectors will loudly warn you of a leak
Fire (and explosion) is mitigated in the main by the cutoff and venting. When lighting a gas cooker, there is usually a requirement to hold the ignition until the flame has caught - and if the flame goes out, the cutoff will stop gas flow shortly afterwards. So the main fire risk when asleep is from leaving flames on - so checking all fire is out before going to bed is essential. No using the cooker as a heater when cold! Just wrap up warm.