No pilot light, no safety valve.
Here in California all the gas space heaters I've experienced have at least had pilot lights. However the older ones didn't have safety valves, so if the pilot blew out (a not uncommon occurrence) you could potentially turn the gas on and fill up the room with explosive fumes - if you had no sense of smell, that is. Later ones seemed to have safety valves, which also have a limited life span and do need to be replaced from time to time (thermocouples, as I recall). And of course the newer ones have more advanced safety features.
Usually the pilot light in the gas oven would blow out in the various rentals I inhabited. Sometimes just closing the door to the oven too fast would blow out the pilot, in one place I rented. The landlady was a very unpleasant person of middle eastern origin, who would first blame the tenant, and then after much arguing, hire drug addicts to do repairs, so I never complained about it. I would fix what I had to on my own, instead.
Oh, yeah, and that rental was a little two story wood frame house. Quite old, and actually a balloon frame, not a stacked frame like modern wood construction. Anyway, the sole heating for the home was an underpowered wall heater in the downstairs living room/dining room area. The place was quite drafty - one of the walls in the living room was sagging so much that a big horizontal crack opened up at chair level, which I wound up patching with plaster just to keep the drafts out. What heat the wall heater put out went straight up the stairs to just one of the two bedrooms. Which was fine when I used it as such, but the larger bedroom was generally frigid as was the downstairs. Fortunately it doesn't get all that cold here but it can hit 32F in the coldest winter days.
I was very happy move out of there after 12 years, and to buy this current house with central heating and with myself as the landlord

.