Slimes actually eat all the very little stuff that big monsters can't really touch and that they don't want to have on them. All those very, very tiny critters, the waste products, the little adventurer bones that always stick between your teeth...
That's why they aren't killed by larger monsters. Larger monsters would rather protect slimes as long as they are doing their job. And being pretty much mindless there is rarely any occurence of normal slimes acting up in any way.
They are living an easy live of eating away stuff from larger monsters, which is why they are delivered their food and don't really have to fight for it. No need to compete with each other, lots of food, being protected by stronger beings, ...
Larger monsters simply breed slimes to be mindless little critters that can't harm anyone, just like humans are breeding animals for different purposes.
That's also why it's so easy to kill them for adventurers. And why you will soon have stronger enemies after having killed lots of slimes. Be careful who you are making your enemy...
But they don't eat us, it's a common misconception. They actually eat gold and treasure -- that's why they're always sitting on a pile of it
. And here I thought they usually ate canned food and the horse it rode in on. $\endgroup$