So what exactly has Becky been up to this whole time? The narrator would really like to catch us up with her but, well, her doings aren't really appropriate for polite conversation.
The narrator makes a now-famous comparison between Becky and the sirens of Greek mythology. Sure she's really pretty sitting on a rock and singing, but only as long as you don't look too deep under the water to see her monstrous tail and the carnage and corpses of her devoured victims.
Take that, Becky!
Within the bounds of politeness, we learn that Becky has been traveling all over continental Europe, seeking out small colonies of British people to live among. Her life is a repetitive cycle now. She finds some people, befriends them, tells them her version of events, they believe her and like her, and then one of two things happens. Either she gets bored with normal, repetitive, daily life, or somehow one of the new friends gets word from London about her background, or the actual deal with Lord Steyne, or something else. Then she moves on to another place.
It's a cycle, but also a downward spiral. Her social standing, and the standing of her friends, keeps getting lower and lower. She starts to drink more and gamble.
Ever the thrill seeker, Becky starts to need a constantly higher order of thrills.
Eventually she sinks low enough to try to get on the stage as a singer. But sadly, at this point her voice has been ruined by the drinking and the hard life she's been living.
Finally, the last straw. One day, in Italy, she somehow manages to get an invitation to a fancy party, and who should be there but...Lord Steyne!
Becky smiles at him and suddenly flashes back to memories of her former glory.
He sees her and loses his, ahem, composure.
The next day she goes for a walk in the fashionable district of town to try to see him, but is instead intercepted by his valet. The man tells Becky that if she stays in Italy, she will get sick and die. (Hint, hint. Her illness would most likely be a fatal case of knife-to-the-throat.) Steyne is still enraged at what happened and will never forgive her.
Becky gets scared and leaves the city.
Soon after this, though, Steyne has a series of fits and dies. His heirs and mistresses scramble over his inheritance and fortune.