When the new aircraft market goes away, the engine will go out of production soon after. The engine manufacturer will calculate how many spares will be needed to support the fleet through the expected retirement, build that many engines, then shutdown everything aside from the normal consumable spares (things like turbine blades and 'life limited' parts). It's simply not cost effective to maintain a production line that's only making a few spare engines. And, even a huge fleet of engines such as the CFM56-5 or -7 won't need that many additional spares - as aircraft get retired those engines are often overhauled and put back into the spares pool. Look at something like the JT8D - something like 10,000 manufactured with many still flying around, but Pratt hasn't built a new JT8D in nearly 20 years.
That being said, the CFM56 is still scheduled to go on new build aircraft for several more years - it won't be going OOP anytime soon.