Here are some signs your elderly parents should not live alone:
Disorientation
While minor memory lapses and forgetfulness are usually benign, disorientation is another matter entirely. If your elderly parent has had even a single episode of disorientation, i.e. not knowing where s/he was, getting lost coming home from routine errands, or is found wandering the neighborhood, it's time to have a professional assessment done. These spells usually increase over time and can be dangerous.
Medication
Are they forgetting to take their medication? Ideally, their meds should be in pill organizers by day of the week. That way it's obvious to see whether or not they're current. Otherwise, you might have to do some sleuthing to see if their prescription matches up with the amount left in the bottle.
General Well-being
How is their overall well-being? Do they appear well groomed, clean, and dressed in presentable clothes? Or do they seem a bit haggard, frazzled, and/or unkempt? Do you notice unusual signs of lethargy, sadness, or anger? These can all be signs that mental faculties are beginning to slip and/or that your elderly parent is becoming depressed. In either of these cases, you will want to consider other living arrangements.
What's in the fridge?
Take a look in the refrigerator and pantry. Are they stocked like normal? Do you see signs that your parent(s) is eating regular meals? If not, a plan needs to be set in place. It is easy for seniors to become dehydrated and malnourished, which contributes to mental instability and physical health issues.
Housekeeping
What is the condition of the interior and exterior of the home compared to normal? If you notice that things are becoming dirty, cluttered, or generally unkempt, step one is enlisting the help of a professional house cleaner and/or gardener. If you notice that both the house and your parent's physical appearance is slipping, it may be a sign that more acute care is required.
Business
If you notice that piles of unopened bills are accumulating where the mail used to be organized and sorted, your parent may need help. In some cases, this is simply an issue of vision changes that need to be addressed. In others, it can indicate your elderly parent is struggling to keep track of dates, or write checks, etc.
If you have any doubts as to whether or not your elderly parent should be living alone, contact a reputable home health agency or talk to a medical professional to schedule a home health assessment and health evaluation. The results will help you create a long-term plan for your parent's well-being.