What goes around, comes around. He who lives by the sword, dies by the sword. These are two common sayings that are the equivalent of Holmes's statement in “The Adventure of the Speckled Band”:

Violence does, in truth, recoil upon the violent, and the schemer falls into the pit which he digs for another.

Holmes is referring here to Dr. Roylott, a violent, evil man who has ended up dead, bitten by the poisonous snake with which he killed Helen Stoner's sister and intended to kill Helen herself. But his dastardly plan has backfired disastrously, and it is Roylott who lies dead, not his stepdaughter.

Even before Roylott killed Helen's sister, he had acquired a reputation for violence. While he was working in India as a doctor, he beat his butler to death in a fit of rage after accusing him of stealing from him.

The lengthy prison sentence that resulted from this brutal act in no way curbed Roylott's violent impulses, as can be seen from how he had one of his stepdaughters killed.

In the end, it was almost inevitable that his penchant for violence would come back to haunt him, would bring about his richly-deserved demise. In attempting to kill Helen Stoner, Roylott was digging himself an enormous pit into which it was all but certain he would fall. But it was only thanks to the ace detective work of Sherlock Holmes that finally pushed him into it.