Can and does.
Almost all cars with automatic transmissions have warnings in the owners manuals about this. Sometimes it will say "No more then 50 miles or 50 mph or severe transmission damage will result"
The problem is that normally when a car is towed the engine is off and with the engine off there is no circulation of transmission fluid inside the transmission to lubricate the internal parts.
People who pull their cars behind motor homes are supposed to disconnect drive shafts to save their transmissions from damage.
Of course short distances, like if they towed your car from where it was parked, should not be too much of a problem unless it was in Park.
Almost all cars with automatic transmissions have warnings in the owners manuals about this. Sometimes it will say "No more then 50 miles or 50 mph or severe transmission damage will result"
The problem is that normally when a car is towed the engine is off and with the engine off there is no circulation of transmission fluid inside the transmission to lubricate the internal parts.
People who pull their cars behind motor homes are supposed to disconnect drive shafts to save their transmissions from damage.
Of course short distances, like if they towed your car from where it was parked, should not be too much of a problem unless it was in Park.