The really fun answer is that using Scripting on pg. 69 of Unwired, you can decide exactly how your drone's integrated (or custom) dog-brain performs decisions like that. You can tell it how long to wait before acting and what to do afterward. Giving it fuzzy logic lets it be flexible (i.e. I haven't gotten a command in 9 seconds, and audio sensors are picking up gunfire at the rigger's location, and tac-net registers multiple hostile contacts, so I should probably go provide cover fire). Otherwise it runs off of a default script (patrol area x, alert if y sensors are tripped, report to z position every 2 minutes), or simply maintain position and await further orders when not being actively controlled.
If you don't expect to need to actively use your Command program, turning it off will save you drain on your System (mostly important if you're also the team's hacker or overwatch). Keeping subscribed to your drone is optional, and your pilot would certainly kick on if that happened (again, probably with a default script if you haven't given it something specific). Maintaining subscription does have the upshot of making more aware that a drone goes offline, gets jammed, or otherwise falls to mischief. Multiple subscriptions, of course, also drain your hardware resources.
But yeah, if you're a 'Mancer? What Mantis said.