If your loved one is at home alone, are they competent enough to realize that there is an emergency, and if so, do they know who and how to call for help?
Ask your loved one what they would do in case of fire, power outage, or sudden illness. Do they know who to call? If they do, ask them to show you what number they would dial. Don't assume that they know how to dial 911. Many times that does not translate from their mind to the right numbers on the phone. Maybe they could dial 911 if that number were posted on the phone with the word "Emergency" taped to the phone, wall or bulletin board. In an emergency, would they be able to keep a clear enough head to know to look at the note to call for help?
If there is a fire, are they going to try to put the fire out; are they going to run out of the house; or, are they going to stand there until it is a dire situation? Do you need to take the knobs off the stove and unplug the microwave to diminish the chance of fire? Most of us can't predict how we would react in these situations, let alone know how someone with dementia or Alzheimer's would respond.
You need to think ahead and plan. Try to prepare your house and loved one for any situation. And realize that there will come a time when it is no longer safe to leave your loved one alone. Having a backup plan could make any emergency or unexpected event less stressful.