Researching the general area of home automation from a mainly DIY perspective, I have yet to see systems that monitor and push alarms based on network failure. Many retail systems will trip automatically if the phone line breaks but if the incoming network provider cable is cut then DIY systems are vulnerable. Are there any integrated solutions for this, other than purchasing dual WAN/LTE routers that allow push notifications? It does seem like a gaping hole in any home security setup.
Most if not all Home Automation systems are not meant to be a full replacement for a dedicated security system. Cheap (relatively speaking) DIY consumer devices are not reliable to the point where they should be used for critical systems.
I am not sure if there are any systems like this, I have never looked into it. But if this type security is important to you, I would suggest that a DIY solution is probably not the right way to go about this. I would think that a professional evaluation of your premises and a professionally installed solution would be prudent.
Gotta agree with @neonturbo. DIY home automation and commercial security systems fit very different needs, with differing price points to match.
Even “real” home security systems are more likely to have a built-in failover WAN connection in case the system’s primary network/phone connection is tampered with.
Could a home automation hub be created with the same feature? Sure, but at additional cost and complexity to setup, and probably an ongoing fee (someone has to pay for the cellular network connection after all).