run-in

Meanings

1. An encounter; a scrape or brush, especially one involving trouble or difficulty.
2. The end-phase of a competition etc.
3. A sudden compression between two coupled railcars when the hinder one is moving faster than the fore one.

1. (not comparable) Having been run in before or behind previous text.
2. (sometimes comparable) Having been run in to seat the parts.

Etymology

Derived from the verb run into. For the meaning "end-phase", it presumably comes a marathon race, where in the final part the runners run into the stadium and complete a lap.