NASA is looking into this with their Low-Density Supersonic Decelerator program.
NASA's Low Density Supersonic Decelerator (LDSD) Technology Demonstration Mission, led by NASA's Jet Propulsion Laboratory in Pasadena, Calif., will conduct full-scale, stratospheric tests of these breakthrough technologies high above Earth to prove their value for future missions to Mars.
Three devices are in development. The first two are supersonic inflatable aerodynamic decelerators -- very large, durable, balloon-like pressure vessels that inflate around the entry vehicle and slow it from Mach 3.5 or greater to Mach 2 or lower. These decelerators are being developed in 6-meter-diameter and 8-meter-diameter configurations. Also in development is a 30.5-meter-diameter parachute that will further slow the entry vehicle from Mach 1.5 or Mach 2 to subsonic speeds. All three devices will be the largest of their kind ever flown at speeds several times greater than the speed of sound.
Together, these new drag devices can increase payload delivery to the surface of Mars from our current capability of 1.5 metric tons to 2 to 3 metric tons, depending on which inflatable decelerator is used in combination with the parachute.
The test model has the test stage embedded in the middle of the inflatable structure:
Note that this only works for small missions (3 tons lander weight). SpaceX's Mars lander (the BFS) weighs more than 100 tons.