This condition is called ventroflexion. There are a number of possible causes one of which is a deficiency of thiamin in the cat’s diet. I’d check that out first. Make sure the diet is a good quality commercially prepared food. You may see a near immediate improvement. Consult with your veterinarian. Other COMMON causes of feline ventroflexion (drooping head) are: hypokalaemia and organophosphate poisoning (veterinary-practice.com). There are many uncommon causes. Please see a vet.
Thirty percent of cats with chronic kidney disease (common in elderly cats) are hypokalaemic. So the underlying cause might be kidney disease but only a few cats show neck ventroflexion.
P.S. There may be another reason for a cat holding her head down, which is why seeing a vet is important.
