Fuel will not magically flow into the engine without air, so i don't know how the engine can suck to much fuel and cut out.
There's a lot you don't know.
Gasoline will burn at mixtures of 8:1 to 18:1. Get it richer than 8:1 and it will quit. Get it even close to that and it will stumble. Some airplanes need some intelligence to manage that mixture properly. The R182 has an O-540J3C5D with an HA-6 carb that has an extremely rich setting at full rich; I complained to the carb makers, Precision Airmotive, and they told me that it was the way Lycoming wanted it for that engine. The engine would start missing and running rough at full rich, carb heat on, on a DA of 4000 or more. Much higher than that and it was blowing black smoke as well.
From the R182 POH that nobody ever reads before complaining about it:
Yeah. With carb heat on you'll have to lean it.
From the expanded procedures:
Look at that. May be leaned above 3000 feet. That would be a DA of 3000, and that's easily experienced on a warm day at a much lower altitude.
In that engine, on a high-DA day, if you use full rich in the runup you will get large mag drops. If you leave it running on one mag the RPM will sometimes continue to decrease. I never let it quit, but it was sure headed that way. Leaning it got normal mag drops.
Edit: There's an AD on that HA-6 carb. It had the possibility of the mixture control valve mechanism coming loose inside the carb and flooding the engine. At least one accident happened due to that. So yes, it is possible to overfuel an engine and kill it.
Another edit: That HA-6 AD addresses the loose mixture sleeve cutting off the fuel flow, not increasing it. Memory getting faint. I had to recall an airplane in flight, headed for the mountains, the morning I received the emergency SB that eventually resulted in the AD. That airplane had the defective version of the carb. Must be 12 or 13 years ago.