For any creature to survive alongside humans, that creature must be able to withstand the ecological changes that humans precipitate. Namely, the creature must be able to withstand being killed at whatever rate humans kill it at, and it must be able to keep getting food even with human hunters competing with it.
The creature would need to exist in a different ecological niche than humans.
One of the major reasons that humans drive large carnivores extinct is competition. Humans tend to hunt large plant eaters, so any animals that have evolved to hunt specifically these kinds of creatures tend to be driven extinct by human competition. A good example of this is the smilodon, a kind of saber-toothed cat. It evolved as a niche predator of large animals like ground sloths and mammoths, but wasn't well suited for hunting smaller, faster creatures like deer. When humans came in and drove their food to extinction, the smilodons followed.
In order to survive humanity, a creature would need a different food source than us. Most likely, if the creature is big enough to eat us, it either eats something that is too big for us to kill, like a large sauropod, or else something that's too dangerous or inaccessible for us to go after, like crocodiles or whales.
The creature must either be too big for humans to kill, or not be the biggest creature around.
Most creatures have a reproductive rate which is closely tuned to their rate of death. Even low-level killing from humans, for example, can be problematic for something like a polar bear that reproduces slowly.
On the other hand, animals like coyotes that regularly get eaten in the wild tend to produce lots of babies to account for the higher death rate in adults. For coyotes, competition with wolves (and predation by wolves) caused higher mortality rates than did people, so killing off the wolves has increased their population.
In order to survive humans, a creature would need to be either big enough to almost never get killed by people, or else not be the biggest thing around. For example, if there were dragons and something big enough to munch on them in the natural environment, humans killing off the dragon munchers could lead to a population boom for the dragons, especially if the former apex predator ate nothing but dragons and ate lots of them.
The predation rate of the dragon munchers would only need to be higher than the rate at which people kill dragons. Any areas with low populations would also serve as dragon population reservoirs, since dragons would quickly reproduce to fill these areas in the absence of human competition for food.
There would probably need to be a more productive environment.
Of course, there needs to be a source of lots of calories for all of the dragons and dragon munchers to be ecologically viable. This has, of course, been the case at lots of points in the past. Dinosaurs grew huge in part because there was more plant growth when they were lumbering around. More plants can support more and larger herbivores, which in turn support more an larger carnivores. A human sized sapient creature which evolved in such an environment would likely disrupt their environment, but probably not enough to kill off all predators larger than themselves. Especially in the untamed wilds, humans could easily be far from the top of the food chain.