funny you bring up this analogy. tons of auto manufacturers these days will license other mfgs' engines and use them in your cars. e.g. a fair number of Ford's cars have had Mazda engines and a fair number of Mazdas have had Ford engines.
Sure. Mazda’s CX-3/5/9 in the aughts and early teens often had licensed Ford engines. The current Ford Tourneo Connect has a wholly VW-manufactured engine.
It’s probably most common when an automaker introduces a new make and wants to save time and capital on developing and getting into production a new engine.