One of the biggest struggles we face as we age is remaining independent in our own homes. As adult children caring for aging parents, we often have these discussions with them. While we know their physical and mental limitations, they do not want to leave the home where they raised their family. If they insist on remaining independent, then the most we can do for them is make their lives safe.
First, have your parents sign up for an emergency response system. This will give them 24/7 access to the police/fire department. If they fall, help is only a button away.
Remove all fall hazards, such as throw rugs and sharp corners on tables. Make sure transitions are smooth between rooms, and install grab bars in the bathrooms.
Set alarms around the house. There are alarms for alerting someone that a pot has been left on the stove unattended, or for reminding them to take their medications.
Do what you can to make their life simpler. This may be different door or drawer handles, a long shoehorn, velcro closures, or a grabber for reaching items from upper shelves.
Make sure they eat right and have regular checkups with their physician. Activity is especially important for keeping healthy. If they have difficulty doing any daily activities on their own, hire help to come in and assist with meal preparation, bathing, etc.
Finally, stay connected with them. Loneliness can cause depression and premature aging. But whatever you do, take care of yourself also. If you don't take care of you, you can't take care of them.