My whole house is covered by a Nest Secure alarm system. At the moment my Nest Guard is telling me "it's offline". But if someone breaks in the house, the alarm will still ring in the house, however I believe I won't be notified on my phone (can't even log into the Nest app), and the alarm monitoring center (operated by Brinks under a partnership with Google) probably won't be notified as well, which sucks. I'd love to test it right now, but my daughter is sleeping and I don't want the alarm to wake her up...
I wonder how often outages occur with other alarm monitoring companies. They certainly do occur, but customers don't have a lot of visibility into them.