It's common practice these days in Android apps to request the user to turn allow the app to run on the background, opening the necessary Android settings page if you want to grant the app access to this. If an addon needs that feature, the app could request this for the addon at moment of installation.
I think you misunderstand what I'm saying. Modern browsers try to host their extensions in a special sandboxed subprocess. At the time I was there, the code in Gecko that hosts sandboxed child processes was completely unable to deal with that host process being terminated; ie Gecko could not recover from that. It has nothing to do with Android settings.
