A stiff cat doesn't necessarily mean it's completely dead, and there's still a chance of saving it if you take prompt action. Cats can sometimes enter a state of apparent death (thanatosis) when experiencing severe stress. You can try gently touching and stroking your cat to rouse them. However, if your cat's body is stiff and it lacks vital signs like body heat and a heartbeat, it's likely beyond help.
A cat's stiff body usually indicates that its vital signs are extremely weak, but it doesn’t necessarily confirm death. When a cat is excessively frightened, it might enter a state of ‘playing dead’ as a way to cope or escape. You may not be able to wake them simply by calling their name; instead, try gently caressing them. The cat will be able to feel your touch and, with patience, they should gradually come around. However, some cats react differently; gentle touch might not be sufficient, and they may remain in the ‘death-like’ state for hours. In such cases, you must take them to a veterinarian immediately to have them revived by professionals. It's important to act swiftly as prompt action could make a critical difference.
Additionally, the cat could also have truly passed away. Carefully observe your cat for any breathing, heartbeat, or pulse. You can gently press on the area over their heart and check for any reaction. It is also important to keep them warm. There is still a small chance that they can be revived. If there is no heartbeat, no warmth in their body, and no response to stimuli, then the cat has unfortunately likely passed away and there is no hope for revival. In such a situation, you need to make arrangements for their aftercare. Remember, early recognition and response are paramount in such critical situations for your beloved pet.