My wife is at last stage of Alzheimer's; she cannot move, eat, drink, swallow. Can she be at vegetative state before end of life?

I am sorry to hear that your wife in is the last stage of Alzheimer's.  It is so hard to see a loved one in this stage.  Go to alz.org website for more information about the stages of Alzheimer's and the type of care for each stage.  There are some great booklets about late-stage Alzheimer’s and End of Life care,

alz.org/care
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God Bless.

Where is your wife living? Is she at home, with you as her main caregiver, or in a facility?

This must be so sad for you. Hugs.

Is your wife on Hospice care? If not, that is something you should definitely consider at this time.