If animals stop reproduction, there will less variety, fewer food options and they will eat each other. There will be no meat for humans and eventually life will extinct from this planet.
The event that would be the result of a species halting its reproducing would be the species becoming endangered and eventually becoming extinct.
Explanation:
Since animals eventually die, the reproduction creates additional animals, in which replace the dead ones. If the species stopped its reproduction, the species would die off because there are no other animals of that species to replace the dead ones.