NASA is planning to bring an asteroid into a lunar orbit. As I understand, it's a tremendous task, even when using high specific impulse ion drives. It seems nearly impossible to safely land one on Earth without using aerobraking: the ion thrusters cannot be used anymore because of fast action required and therefor additional rocket engines with super reliability, high maneuverability, vast thrust power variability and huge amounts of fuel have to take over (seems pretty expensive and risky). Aerobraking would greatly reduce the total delta-V requirements, risk, price and landing complexity. But all the heat shields I've seen are robust, solid and far away from "flexible".
Are there any atmosphere entry protection capable cloths available? Would they tightly surround an asteroid without any holes and leaks under atmospheric pressure alone or some junctions before entry would be required? Could these cloths be strong enough to survive tearing force from the parachutes above or the parachutes should be anchored to the asteroid itself?
By the way, I'm thinking about commercial (not scientific) purpose landings of super-valuable space rocks, therefor a "safe landing" can be declared when the asteroid touches the ground (not burns up or shatters above ground) and it's parts remain within a small radius (1km or mile). I mean, it can reach the ground at 100 m/s and leave a fair crater, but as long as we can collect all the valuable material (platinum, may it be) scattered in a reasonably sized area, it's okay. Maybe even the parachutes aren't a necessity then, if terminal velocity of an asteroid (now meteorite) is small enough for this task (is it?).