The reason the Landlord and Landlady gave up kung-fu in the first place is because their son was killed in a fight.
The romantic subplot, believe it or not.
Sing, as a young boy, attempted to defend a mute girl from some bullies, who were in the process of stealing a lollipop from her. He believes himself a capable kung-fu warrior, but he is unceremoniously beaten and humiliated. He decides at that moment that trying to do good just isn't worth it, and sets out to become a criminal.
When he meets that girl again, they've both grown up. He, a homeless criminal wannabe, and she, running a humble refreshments cart. Sing is in the process of stealing money out of the cashbox when she reveals that she still has the lollipop the bullies were trying to steal from her, and which she had tried to give him in thanks all those years ago, faithfully preserved. She offers it to him again, still thankful that he tried to save her, but Sing freaks out, knocking it out of her hand and breaking it in the process, before running off.
After The Beast beats Sing within an inch of his life and the Landlord and Landlady rescue him, they ask him if he wants anything. He only has enough strength left to draw a lollipop with his own blood before passing out. Meanwhile, the girl is trying to reassemble the broken lollipop. She picks it up, thinking she has succeeded, only for it to fall apart again.
Despite the three heroes' efforts that saved the people of the slum, they are eventually banished from their homes (due to unpaid rent.) Although they promise to fight against and also with each other another day, their lives are cut short early in the film.