Elon Musk said it himself:
Universe Today believes Musk is possibly referring to a ballute—a hybrid balloon-parachute invented by Goodyear Aerospace in the ‘50s—that could slow down and stabilize the upper stage as it descends through the atmosphere. Retrieving and recycling lower stages of SpaceX rockets has reduced the massive launch cost. Being able to do the same with upper-stage boosters could make it even more affordable while cutting down on space junk, but figuring out exactly how to do that without any disasters is no party.
“What happens when these things slow down to landing velocities?” University of Maryland engineering student Quinn Kupec told Universe Today. “If your center of gravity is offset significantly behind your center of drag, as would be the case with a returning upper stage, it can get unstable. If the center of gravity of the re-entry vehicle is too high, it can become inverted, which is obviously not desirable.”
Which is why Kupec tweeted this to Musk:
Anything as huge as a Falcon 9 or Falcon Heavy would come crashing down to Earth without something forcing it to decelerate. The velocity of an object plummeting through the sky is measured by a ballistic coefficient, and what Musk wants is obviously a low ballistic coefficient if he has any prospect of recovering that upper stage in one piece and preferably not inverted or in flames. He will have to lower the speed of the booster to the point that the heat firing up from reentry will cause no damage. Meaning, that disembodied piece of rocket needs to be an ultra low ballistic entry coefficient decelerator.
This is why the “party balloon” Musk has in mind can’t burn up in the atmosphere.
About that balloon. It sounds like it would make a booster just float down to the surface. The reality of that is slightly more complicated, explained Professor Dave Akin, also of the University of Maryland. “The balloon would have to be 120 ft. in diameter, and made of a high-temperature fabric,” Akin predicted about what it would take to pull off what Musk is dreaming of.
Even if that gets figured out, nobody knows what this means. Yet.