+1 on this.
However a few enhancements.
First layer, exterior lights activated by motion detectors. Scares away the amateurs. A drive way ding dong is good idea.
Second layer enhancement; magnetic contacts on all windows, doors, and or glass breaks shock detectors, another motion detector, and a curtain type detector wired to sound an alert when large mammals are near the exterior perimeter. when people are home, or away, depending. I prefer to use exterior curtain only when the alarm is in the stay mode vs away mode. Utility worker, or passing animal have set mine off.
Two way video intercom. That way the senior person don't have to deactivate the perimeter curtain and give interior home access to strangers.
Third layer; The FOB panic button has its limitations. My wife wanted one. Most folks leave them in the location they keep their house keys. I prefer panic buttons in at least three locations. Make sure the panic, and alarm alert not only trips a siren, but sends two signals to a Central monitor, one via phone, one via radio or cell. Go ahead cut my phone line. A strobe light is an option.
Bad guys hate attention.
Forth layer; (optional) A dog to sound the alarm. I prefer dogs that bark, and don't bite. To much liability there. In addition, the a dog requires maintenance. Can't leave them alone for months, like you can with a monitored alarm. Dogs are a more of a nuisance then a blessing to senior people.
Fifth layer; Pepper spray. I don't know if this is a great idea, as many senior people have respiratory issues. I could include wasp spray, but to avoid an on line pissing contest, I won't.
Sixth layer (SHTF); A firearm. A hammerless double barrel coach gun in 20ga loaded with at least #4's. Tang safety.