Hi, I saw a Nat Geo documentary on the mars rover program, and apparently they had this problem with the chutes called "Shrimping". The lines wouldn't get tangled, and the chute wasn't streaming, but the circular canopy would kind of fold on itseld, with several points on the circular canopy bunching around the centre, without touching.
Of course this reduced the available drag.
The engineers acted like they had no clue why this was happening, but that might conceivably have been staged for the camera's benefit (you know, a bit of a cliffhanger).
Anyway they ended up restricting the vent hole and the problem went away.
The chute was of a design called "Disc-Gap-Band), I don't know if the problem occurs with any other kind of canopy.
All google searches turn up either references to Forrest Gump, or to the sexual practice...
If anybody has any information on this, it would be greatly appreciated.