The caracal shares some of its habitat with larger predators such as leopards, lions and hyenas. Sometimes they fall prey to these larger animals and are eaten by them. Wild dogs also pose a threat. That is about it in answering the question in the title.
However, the caracal is a spirited animal. In Israel, at a vulture feeding station, a caracal was eating a donkey carcass. To protect his prey he chased off a couple of young hyenas. One of the hyenas was twice the weight of the caracal. This story is told in the book “Feeding behaviour in caracal Felis caracal by JD Skinner 1979.
Another story highlighting this medium-sized cat’s spirited character concerns the Kruger National Park. Pienaar, a biologist, writes: “the head of one of these spirited animals (caracal) was found near the Tsende picket, where it apparently disputed the carcass of a waterbuck calf with seven lions.” (Pinnaar, U. De V. Predator-prey relationships amongst the large mammals of the Kruger National Park 1969).
Although the caracal is occasionally attacked and eaten by larger predators it is no push over and I’d expect it to avoid being eaten a lot of the time.