Autos usualy have a hydraulic transmission, basilcy two impellers roatating in a liquid. The faster one spins the faster the other spins, its kind of like driving arround with the clutch pushed in 5%. At motorway speeds the transmision locks (the two plates get pushed together) to improve efficiency.
After that you have a series of planetary gears (think of it like a big hammersmidt) with hydraulic circuits regulating which ones are in use, put your foot down and pressure builds up, opens a valve, drops into a lower gear, reach a constant speed, pressure drops, valve closes and engages a higher gear. So in effect when you'r in 3rd (for example) your also in 1st and 2nd as well.
Modern ones do it all electronicaly.
Even more modern 'semi automatics' are just the normal (occasionaly dog-bone) gearbox with an automatic shifter.
So yes, its perfectly possible to have an automatic stuck in gear, it wont stall as the box just drops it into 1st and keeps pulling, and the ECU probably wont let the engine cut out whist your moving (you'd destroy the cat for a start)