May I suggest that you consider a professional medical home alert system. She might not want an aide intruding on her privacy, but might consent to a system that allows her to push a button for help. They also have systems that monitor the person and raise an alarm if signals deviate from normal. You can't monitor her 24/7/365, but a medical alert provider can. And they are trained to know all the signs of distress -- the big ones and the subtle ones -- and to immediately dispatch trained medical help.
Your relative may also be at a stage where her independence is more important than her security or longevity. I hope that doesn't sound cold, it's intended as quite the opposite. I had a relative who understood he was taking a risk, but was honestly ok with it because he felt that everyone was going to go sometime, he'd lived a good long life, and when it was his time, well, he just wasn't worried.
Whatever you decide, I wish you both luck and strength. Taking care of aging relatives is a labor of love, but it is a labor. You're a good person for caring, and she's lucky to have someone who does.