I have a Trace (now Xantrex) 4048 inverter, and I wouldn't have known this before reading the manual. It has a mode called 'Low Battery Transfer', or LBX mode which connects your loads to the inverter from the battery bank when the batteries are sufficiently charged, and then to the grid when the batteries are depleted. To quote from the Trace manual:
"Low battery transfer mode is an alternative way of operating "off the grid" using the utility for backup power instead of a generator. The system essentially operates as a stand alone power system, independent of the utility grid. When the system is no longer able to keep up with the power requirements of the AC load, discharging the batteries to the LOW BATTERY TRANSFER VDC setting, the inverter connects to the utility grid. It then feeds utility power directly to the load and recharges the batteries. When the battery voltage reaches the LOW BATTERY CUT IN VDC setting the inverter disconnects from the utility grid and once again operates the AC load from the batteries. Since power is never sold back to the utility, this configuration does not require utility approval."
One little annoyance with this mode when your intent is to charge your batteries from solar or wind is that the battery charger kicks on when the batteries are low, and the programming only allows you to turn the amps down to two amps, and adjust the charge voltages down, not turn the charger off in this mode. I believe that the grid tie outback inverters have a similar mode. Hope this helps, Rich