It doesn't work like trap. The park's population is supplied, either by the resident or through breeders. It will most likely be isolated from yukkuri population outside.
Especially true for abyuser who enjoy corrupting and killing innocent yukkuri. Have to keep the product's purity and not risk them contaminated by random strays.
It's interesting to think about, because the average view of yukkuri is viewed as below-average, but...
The park is still there. There's still trees, grass, bugs, etc.
This kind of defeats one common logic -- that yukkuri just breed until there's a million of them (like roaches or something). This shows they can actually reach an equilibrium with their environment, even if it's enclosed.