I've seen this happen with a clogged fuel filter. The pump is at the bottom of the tank generally and the weight of the gasoline helps the pump do it's work. As the weight comes off the pump is less able to force the gas through the dirty filter. Couldn't hurt to change it anyway - it's something most people forget about until it's so bad that it stalls the car.
Just do it outside. The first time I changed one I did it in the garage and got high as a kite
