Many modern systems also have the capability of sending you a text message with whatever change happens in the system – alarm somehow turned off, water alarm, smoke, carbon monoxide, break-in, motion detected, etc. (if you have each of those devices installed). If you’re nearby you can get home quickly. If you’re far away, you can either call local police or a trusted neighbor. Personally, I like the wireless systems with a cell-card in the base unit that will call “home” to the security company immediately with any alarm of any sort, regardless of whether the home’s power is on or off. We’ve been notified via text message while 50 miles away of a power failure at the house (thunderstorm produced), and then a few minutes later when power was restored – all within less than a minute of the events. We’d get the same with any of the above events as well.
The nice thing is that such systems may or may not include police/fire notification – that’s the owner’s choice (or circumstances). Yet the personal notifications can still come, including video if you’ve got cameras, to your phone, as long as you’ve got cell reception (our system, Simplisafe, uses a choice of Verizon or T-Mobile for their unit’s transmitter, which is independent of whatever cell system you use).