An odd question, yes, but a question I am asking anyway. I have a group of feral cats that lives in a cave system. They've lived down here for generations, and survival of the fittest weeded out the builds that were unlikely to survive. Question is, could cats sustain their basic needs, off of only what is in the caves? These cats are of human intelligence, have extremely primitive technology. As a bonus, you can also add what mutations and genetics would aid a cat in cave survival (Real life mutations and genes).
With no humans to domesticate, they'll have to hunt their own bats.
Which proliferate by the thousands in caves in many parts of the world.
Some species are blind, living in deep caves without light, so these cats may have unusually large ears, and hunt by the splashes and plops they make breaking the surface.
I think your cats may can survive by hunting bats, besides I think @L.Dutch may be thinking about deep underground ones rather than caves, beside you say your cave is not blocked, which doesn't mean other animals beside your cat don't go outside to hunt, unless I'm mistaken and it includes other animals too?
Also I have seen feral cats hunt bats many times, even inside caves or usually near the cave's mouth.
Human Intelligence is the most overpowered skill you can give to any animal and it's arguably the most powerful skill ever--it's what's enabled humans to dominate the world. This is why I'd say: As long as it's thermodynamically possible, yes, your cats can survive.
To elaborate: living creatures consume energy, measured (for example) in Calories. If a creature eats more Calories than they burn, they survive. If a creature eats less Calories than they burn, they will eventually die, probably before procreation. This means for your cats to survive multiple generations, you need to introduce energy into the cave system somehow. Some ways this could be done:
Hunting non-cave creatures: mice or other small prey animals consume food outside, wander into the cave, and get killed and eaten. Requires reliable and high "wandering in" rate
Farming: certain cave sections have skylights where sunlight pours in. These patches of light are used to grow plants (although I'm not sure if cats would be ok with a strictly vegetarian diet). These plants could also be used as food for domesticated animals, which are eventually eaten by the cats
Fishing: a surface river goes underground and passes through the cave. The cats can use nets or other fishing strategies to catch aquatic life and then eat it
Fungal farming: provided the cats have some sort of abundant biomass source, mushrooms and other fungi can be farmed and consumed directly or used to feed livestock. This has advantages because the fungi do not require sunlight.
Pre-supply: some food preservation methods can keep food edible for a very long, if not indefinite, time. For example, maybe someone stored tens or hundreds of tons of pemmican in the cave before sealing it. This could feed many generations along with possible livestock or fungal farms as desired.
The food chain inside caves is fed through the few organic matter which drips inside the environment. Therefore it cannot sustain large organisms.
The largest cave organism I recall is a sort of newt, way smaller than a cat. If your cats have to sustain themselves only with what they can forage in the caves they will be forced to scale down to a similar size.
Anything bigger would probably starve.