Your mother is probably losing weight because her intake has decreased. The neck hyperextension comes from lack of exercise and thus limited joint range of motion. If her caregivers or even you, exercise her joints, further decline can be prevented. Difficulty with aspiration and choking is a characteristic of the End-stage of AD in many repects. A swallowing study would identify the problem.
Aspiration leads to pneumonia and death eventually, but it can be a seemingly never ending cycle.
You can continue feeding her orally with thickened liquids and pureed foods, trying to prevent aspiration. She will eventually get pneumonia, and you may choose to treat it, and start over again. In the mean time she will continue to lose weight and her skin integrity will be in great risk of being, or will be compromised. That is a very difficult road to go down unless she gets excellent care, which the nursing homes are not staffed for. This is all beside other medical problems she may have that affect her quality of life.