Soft muting small speakers quickly
That sort of depends on the amplifier in the module. 

With lack of other information, safest is a small relay to either switch in/out an extra load resistance when the power drops out. This is best done with a separate control line other than the power line to the AMP so you can sequence the relay around the power application and removal.







simulate this circuit &ndash; Schematic created using CircuitLab

UPDATE: Schematic updated to use a photo-relay and show differential speaker drive resistor connection.