During the korean war what prevented the southern part of the peninsula from falling permanently to the invading forces?

I might be wrong but during the war the US helped the south push the north back but later the People's Republic of China joined the war because they thought the war was a threat to their land and because of that they pushed back until only the south tip of korea but UN forces help push back against them and we ended with no tearatory gained or lost some people called the war pointless hoped it helped

It's poopjrjrkkkeoeoso