I also heard of a second-hand market and renting even for engines, could anyone tell me how it works? Is it not highly regulated for obvious security reasons, and if so which institution controls it? Can engine manufacturers not oversee such a market to avoid dubiously deadly contraband?
There are two basic systems for spare engines. First is obvious - the airline/operator will typically keep a number of spare engines to support their needs. That number will be dependent on the size of their fleet. But there is a second pool of spares which is owned and run by the engine manufacturer. This is used to support small operators who don't want to maintain their own set of spares, but it is also used to support operators who unexpectedly 'run short' - either do to bad luck or poor planning. The number of engine manufacture 'pool' engines is increasing with the growing move towards 'power by the hour' - where operators don't own any of their engines - they lease them from the manufacture and pay a rate based on usage.
When an aircraft gets scrapped or otherwise removed from service, the engines are usually removed - at which point they can also be scrapped (there is considerable scrap value in just the materials, and some parts can be re-conditioned and reused), or overhauled and put in the spares pool.