If your automations are coded sufficiently, then the current one may fail if the browser crashes, however your next one should succeed as it should start the browser back up if it is not running. The failure would be detected by your automation flow (i.e. probably a timeout getting to where you are trying to navigate). You'd display that to the user so that they could correct the problem.
I generally have a start/login automation that returns a success if the adapter is running/logged-in or if it detects that it is not, performs those steps. I add it to the beginning of my main automations so that they will work regardless of whether the adapter is running,