Does anyone ever think their loved one is deceased if they are in a very deep sleep?

LOL.... I think it likely crosses every caregiver's mind under similar circumstances. Part of coping for me was to have a plan in place for such an eventuality, once mom was accepted into palliative care (our version of community hospice) and listed as an expected death in the home it was a relief to know who to call. I think you can reach a point where you are at peace with the thought of them dying, and maybe even are a little disappointed when you realize they haven't.

Not an abnormal fear.
My Husband would sleep soundly sometimes and the though did cross my mind on occasion.
Is your Mom on Hospice? If so they can help you with watching for signs of EOL (end of life) And it will give you someone to call if you have any questions. And if she dies die unexpectedly you can call Hospice and they will have someone come right over and they will make all the phone calls that need to be made.
But if you do walk in and your mom has died take comfort in the fact that she died peacefully and is no longer in any pain. A peaceful death is what we would all hope for.