Why would the nurse say "your mother is dying"?
Reading your question, I would say that it sounds like you were caught off guard by the nurse's comment. I don't think she meant to scare you or shock you, but she was trying to tell you from experience what she sees. Being a nurse myself, I know that we are trained to see the signs that people are dying long before they actually do. There must have been something that she noticed about your mother that makes her think that she is not doing well. Perhaps it is the rapid decline you talked about. Many people with dementia do not have the ability to bounce back from major illnesses, especially in the later stages of the disease. Maybe she feels that your mother will not recover from her decline, but will continue to worsen, which means she will eventually die. She wants you to be prepared for this.
My reaction to this comment would be to listen to what the nurse said, and schedule a time to talk with your mother's health care provider about it. I know that many doctors are not good about talking about death and dying with patients and their families, as it is very hard to do. So, you may have to take the first step. I would let them know what the nurse said and see what their opinion is on the matter.
Make sure all of your mother's affairs are in order. If your mother is still able to have meaningful conversation, have the doctor talk to her about what she wants regarding hospitalization, resuscitation, feeding tubes, etc. This all should be documented so that her wishes will be respected. If she is indeed dying, and her doctor thinks she is in the last 6 months of life, she may be a candidate for hospice. If you can, it is also a good time to make funeral arrangements, so that when her death does occur, you don't have to deal with it then.
As for you, it may be helpful for you to deal with all the emotions surrounding the fact that your mother is declining rapidly and may be slowly dying. Please know that there is support available, especially through religious organizations, your local Department of Aging, and some Hospice Organizations. I would encourage you to reach out if you need help. I wish you luck.
Thank you for the expert advice! To add to to Ms. Serafin's answer, Caring.com has a Senior Care Directory where you may search for local resources mentioned above: E.g. Area Agency on Aging, hospice care providers. Here are a few links to help start your local search for resources:
2.) Local Hospice Care Providers

