I've always knew that the winglets on an aircraft provide lift. But what would happen if a winglet disconnected from one wing while a winglet was on another wing?
this actually happened to the Rutan around-the-world flight, where one winglet was shaved off against the runway pavement during the takeoff roll. the pilot then stabbed the controls to overstress the remaining winglet, causing it to break off during climbout. the purpose of the winglet is to increase the apparent span of the wing by blocking airflow out from under the wing and over & into the airflow over the top of the wing, so an aircraft with one winglet on and one off would perform as if the wingspans on either side of the fuselage were several feet different.
One a modern airliner, the only conceivable danger would be if it hit any of the tail surfaces on its way down.
A 747-400 is despatchable with one removed but not two (I don't know why). There is also a fuel penalty factor but its nothing major.