Literal meaning : The lotus root snaps but its fibers stay joined.
Ever had a lotus root dish in China? It’s absolutely delicious but when you bite into it, you can feel its silky fibers stretch out with the piece on the fork/chopsticks. This Chinese idiom usually refers to romantic relationships to mean : “still in contact though apparently separated.” Think about someone you apparently broke up with but still keep in touch with.
Sentence with 藕断丝连：
Translation: After you break up with someone you shouldn’t keep in touch with him, but you two are still communicating despite the break up.