Try airbags - from Wikipedia:
The design is conceptually simple; a central "Airbag control unit"
[25] (ACU) (a specific type of
ECU) monitors a number of related sensors within the vehicle, including
accelerometers, impact sensors, side (door) pressure sensors,
[26] wheel speed sensors,
gyroscopes,
brake pressure sensors, and seat occupancy sensors. When the requisite 'threshold' has been reached or exceeded, the airbag control unit will trigger the ignition of a
gas generator propellant to rapidly inflate a
nylon fabric bag.....
.....Typically, the decision to deploy an airbag in a frontal crash is made within 15 to 30 milliseconds after the onset of the crash, and both the driver and passenger airbags are fully inflated within approximately 60-80 milliseconds after the first moment of vehicle contact.
So airbag is 0.06 seconds fully inflated after event. I see no reason a rocket propelled parachute with airbag inflating outer ring could not be out in 20 times this figure (1.2 seconds from accelerometers detecting free fall)