Who's to say the light saber ended up in the same tube as Luke?
Let's just say it did, then where was it when Luke got to the trapdoor? And for that matter it still would've fallen to Besbin and shattered.
Bespin. Also it's a gas giant, so there's no surface per se.
I suppose it would do whatever Lightsabers do when they get too close to the core of one of those.
Yeah people say Besbin's a gas giant but it certainly doesn't look that way from space nor should you be able to breath in the open air on the cloud city.