http://starwars.wikia.com/wiki/Anakin_Skywalker’s_second_lightsaber
Shortly after this, Luke carried the weapon with him to the Cloud City on Bespin in a bid to rescue his friends from Darth Vader. Engaging the Sith Lord in a lightsaber duel, Luke demonstrated his vastly increased skill with the weapon, impressing its former wielder. Ultimately, however, Luke’s lightsaber hand was sliced off by Vader and fell, along with the lightsaber it carried, into the depths of Cloud City.[17]
The lightsaber, still clutched by Luke Skywalker’s hand, had become lodged in one of Cloud City’s lower air shafts and eventually was recovered by a maintenance drone. The drone deposited the hand and the lightsaber in Smelting Core D. There, it was discovered by Groggin, the Smelting Core’s supervisor.
In addition (and more importantly), I just watched the scene and there’s nothing to suggest the lightsaber fell out with him. There were even multiple shafts at the bottom so it could have fallen into any of those.
Next topic.
Clever attempt at a selective cut & paste. Let’s scroll down some more and copy more of your “source” wiki article:
Engaging the Sith Lord in a lightsaber duel, Luke demonstrated his vastly increased skill with the weapon, impressing its former wielder. Ultimately, however, Luke’s lightsaber hand was sliced off by Vader and fell, along with the lightsaber it carried, into the depths of Cloud City.[17]
The Emperor’s trophy (3–9 ABY)Edit
The lightsaber, still clutched by Luke Skywalker’s hand, had become lodged in one of Cloud City’s lower air shafts and eventually was recovered by a maintenance drone. The drone deposited the hand and the lightsaber in Smelting Core D. There, it was discovered by Groggin, the Smelting Core’s supervisor.
Groggin had no use for the hand and decided to have it incinerated while he would keep the lightsaber, which he planned to melt down. However, the arrival of Darth Vader in the smelting facility prevented Groggin from taking such action. After a round of aggressive negotiations, Vader left the facility with the hand and the lightsaber in his possession. Though he had other plans for the hand and the lightsaber in mind, Vader was compelled by Palpatine to bring the two items to the Mount Tantiss storehouse on Wayland. There, the Emperor made Vader turn Skywalker’s hand and lightsaber over to him.
Six years later, the mad Jedi clone Joruus C’baoth ordered that a clone of Luke be produced from the limb, and that he be armed with Anakin’s old weapon. When Skywalker arrived, leading a New Republic strike team to destroy the cloning tanks of Wayland, he was forced to fight the clone, which was being controlled by C’baoth. It was ultimately killed by Mara Jade who then used Anakin’s old saber to kill C’baoth himself. Upon the team’s return to Coruscant, Luke presented her with the weapon as a gift.
So we go from canon to EU tripe. And we all know the EU was jettisoned (thankfully) by Disney.