Install switches in bathrooms that when pressed would raise an alarm throughout the house. This is to indicate that someone needs help in one of the bathrooms. This becomes especially useful at nighttime because then people are in their own rooms and if someone hasn't got their phone in the bathroom when they fall, it would be extremely unlikely that it is noticed.
These would ideally operate on more efficient hardware than an RPi because that would make deploying them and powering them with AA cells a much more achievable and long-lasting task.