What happens with garage door control if the internet connection stops working?

Using LiftMaster solution

If the user's internet stops working, they should use their local remotes and controllers to operate their garage door. With LiftMaster MyQ garage solutions (i.e., Internet Gateway or Smart Garage Hub), the user cannot remotely control their garage doors if their internet connection drops since these devices rely on a broadband connection for control. 

If the user's internet stops working, the last known state of the garage door operator while internet connection was still active displays on the Alarm.com customer website and app. The current state of the garage door may be different if the garage door moved after internet connection stopped working.

Using Linear Z-Wave solution

Linear Z-Wave Garage Doors operate using Z-Wave and have internet connectivity through the Alarm.com cellular network. Therefore, the Linear Garage Door opener still operates if the user's home internet connection stops working.