Max, this isn't a stupid question at all. For years, I would just leave the stove screwed onto the canister over night, or for as long as I would be at the same campsite. Then one time, my silly partner left the "volume knob" slightly open just before he hit the sack, and all the fuel escaped overnight. We were in a bad way the next morning--no coffee, cold oatmeal, etc. Fortunately, we were headed back to the truck that day.
Now I prefer to unscrew the canister and replace the plastic cap that came with it, and place the stove in a Ziploc freezer bag in case it rains overnight. When packing up the next morning for a hike to the next campsite, I disassemble everything and put it in my SP 600 pot, which then goes into a custom cuben bag for secure storage.