What does Buddhism say that the laity should do when someone injuries them?
It is up to each situation. Some case running away is proper, but some case negotiating is proper, etc.

The theory is "The buddhist people will try to keep 1)own benefit, 2)other benefits, 3)public benefit, 4)this life benefit, 5)next life benefit, and 6)nibbāna benefit. They try to keep whole 6 benefits, no bias."

Methods, to keep benefits, are multiple up to consciousness management ability of each person.