He is 80 years old, single, drinks beer heavily, won't agree to be tested for memory issues, is verbally abusive to his daughters and has threatened to kill them in email messages. The next day all is well for a day or two then back to the same negative person. We don't know if he is drunk when he sends out the vicious attacks or if it is his mind due to Alzheimer's and possibly vascular dementia.
Is this a friend, neighbour, relative?
I would not be helping one little bit. Let APS visit if you deem necessary.
A neighbor that either threatens you or fires his gun? If so contact the police.
Next time you get an email, or the person that is getting them gets one contact the police and file a complaint.
Is this a relative? If so at some point try to get the firearms away from him. Either when he is out of the house.
Let them know the man has multiple guns in the house and the family considers the threats to be real.
Also mention the drinking.
My grandfather had dementia and wasn't violent, but he was hallucinating. Seeing people looking in the windows, people in trees. In our case we just sneaked them out of the house. He had called police before to report people in the yard, and we were worried he'd be outside waving a gun around. Even if it was unloaded, cops wouldn't know that. He stayed mad at us until he died about that, but we had to do it.
I'm not dissing the police but they aren't trained to deal with mental illness and dementia and there are no guarantees about what kind of officers will be sent or how confrontational the man in question might become.
This way, he gets to keep his guns. It is his right.
One of the major challenges we have as caregivers is trying to get Mom or Dad to stop driving or give up the firearms when they become more dangerous to them than other people who may want to hurt them. Unfortunately, Mom or Dad can still be competent (and able to pass competency testing) while denying certain facts of life and not making good decisions. As my father's vascular dementia progressed, he came to a point where his quick temper and the presence of a firearm on his person came to greatly concern me. I figured he was most likely to shoot my mother when she angered him over something stupid (like the thermostat setting). Dad had enough guns and enough ammo and was still active enough there was no way to remove them and be sure he couldn't replace them and I wasn't ready to challenge his competency just yet. So I got his personal firearm one night when he was sleeping and trimmed the firing pin (and confirmed it would no longer fire) and replaced it in his room. This did not really solve the problem since he still had access to his other firearms, but I thought he was most likely to shoot someone because of his mental state with the pistol he carried on his person. It also took away his ability to defend himself from someone wanting to steal his medication (the primary reason for home invasions and push-in robberies of the elderly in my area). Later when I challenged his competency and became his guardian, I removed all the firearms along with the military knives and swords.
There are no perfect solutions to this problem. I would recommend challenging his competency if he is threatening to kill family members or anyone else. I would not call the police because if he threatens them with a firearm the police may shoot him; much less risky to have a constable deliver a court order informing him of the competency hearing. One of the things dementia does is remove or at least loosen the mental governors we have limiting our behavior. We see it first in our loved one's language, then in their actions. In my Dad's case, before I needed to address firearms I needed to make sure objects with a heavy throw weight weren't around and restrict his access to household chemicals. Once the lifetime filters on actions begin to lose effect, you cannot know when someone with dementia will suddenly decide to take some action, most likely one you never considered at all.