My elderly neighbor has Alzheimer’s. She recently left the hospital after a fall. Her husband/guardian was told she needs support 24/7 and was not to be left home alone. He frequently leaves her to walk the dog down the street, work in the field, plow, etc.
Staying in the house or in the room with someone will not prevent falls. I was walking just behind my mother when she last fell in our home. Although some Alzheimer's patients may want to wander outside the house, many do not. Depending on your neighbor's stage of dementia and mobility, she may be fairly safe alone in the house while her spouse is outside.
I understand your concerns but would encourage you to approach your neighbors with a helping hand and try to contact their children or other family before approaching APS. When we became aware our 72 year old neighbor was leaving his bed bound 96 year old mother alone during shopping trips, we gave him a list of people willing to sit with his mother for 2-4 hours at a time. With his permission, a crew came and gave his house a spring cleaning one day too.
There's very little you can do to keep someone from falling unless you have then in a bear hug all the time. Since even standing next to them, if they fall by the time you react they are already down. It's dealing with it afterwards and not leaving them on the ground for 10 hours.
Bottom line is that he WAS told she should not be left alone because she has Alzheimer’s and is a fall risk and he is doing just that regardless, for whatever reason. She may be difficult to deal with and he is, in effect, escaping. Out of sight out of mind and all that. Offer your help first and try to ascertain why he’s leaving her when he was told not to. I wouldn’t call APS right away, but if he is not accepting of your help or anyone else’s, you may have to alert them.