Presence for safety is risk mitigation. A caregiver in the home, watching while something risky happens, so that when something goes wrong there's someone there to help. Whether you need it depends on the level of risk and how well the person understands that risk.
Short-term presence during risky activities
Sometimes a caregiver is there for a specific activity the person wants to do on their own, but where a fall or other incident is a real possibility. Independent people at high risk of falls often want someone in the home while they shower or bathe, just to feel secure. People with mobility issues or fatigue may need a caregiver along on errands and shopping trips to carry bags and steady them on their feet.
While the caregiver is there, they're usually doing light housekeeping or other tasks in the background.
Ongoing presence when insight is gone
Ongoing presence for safety is a different situation. It's indicated when someone repeatedly puts themselves or others at serious risk and doesn't recognize the danger. Think of a person living with dementia who wanders away from home, someone who tries to walk unassisted when they can't do it safely, or high-risk behaviours like climbing on furniture or unsafe use of the stove.
In these cases, the primary reason the caregiver is in the home is that the leaving the person alone isn't safe. In addition to the primary job of supervision they are also completing light housekeeping, personal care, meals and other tasks as required.
Balancing safety with independence
This is usually the hardest part. Where's the compromise between someone in your home (which feels intrusive) and the alternative (a fall in the tub, a serious injury, or a move into a group care residence)?
The question to ask: what's the least intrusive way to mitigate the risk? Sometimes that's a webcam or a call alert button. Sometimes it's a motion sensor. Sometimes it really does need to be a caregiver in the home. Start with the lightest option that actually addresses the risk, and add support as the risk grows.