If a person is hit/struck by a vehicle then we would usually say that they have been "knocked down". If the vehicle actually knocks them down and then passes over them, then they have been run over.
"Run in" with reference to a vehicle is a phrase which has not really been used since the 1970's.
It used to be that, when a car was new or had a new engine fitted, the moving components in the engine were quite "tight". Therefore, the owner would be advised to keep his speed relatively low for a certain number of miles until the engine had become "run in." I am unaware of there being a need to run in modern engines because of developments in engine manufacture.