Q:

What happened to Bespin after the events of Empire? 

Presumably the Empire took it over, but did they shut it down?  Did they continue to mine the valuable Tibanna gas, even though it was technically illegal?  Was there a repossession auction?  Did Lando, either himself or through rebel agents, attempt to reclaim or repurpose any equipment?  What about the citizens who didn't escape? 

A:

Within the new official canon of Star Wars (e.g. The 11 feature films, Clone Wars TV series and movie, Rebels TV series) there's no further mention of Cloud City or its 5 million inhabitants beyond the end of The Empire Strikes back. 

Elsewhere in the EU, there are extensive references including a visit from Jabba the Hutta's father (who becomes Governor for a few hours), an occupation by Grand Admiral Thrawn's forces, recovery by Lando and a strike force and the city's eventual fall into ruin after (what else!)  a trade dispute. 
You can read a potted history here on the Star Wars Wookieepedia website.