Same thing's happened in the Art world for years.
Somebody nicks something worth say £10M - that's what the premiums were paid for, and that's what the insurer has to pay out on.
Thieves can't actually shift the art for £10M though - traditionally you'd get a very small percentage to give it to a hooky investor who'd look at it in his vault, or just used as portable collateral for criminal deals.
Point is - painting is only worth £10M to the insurer who paid out the £10M.
So art recovery specialists exist.
They'll 'manage to recover the art through opaque means' for say 20% of the value. Now maybe they're more resourceful and have greater powers than our police services... or maybe it's just that they can discreetly say they'll hand over a million in cold-hard-cash for the recovery, no questions asked.
Everybody's happy - except I guess people paying premiums on their art..
Owner gets their art back, insurer saves 80%, recovery specialists have a million profit, criminals have cash and nobody still coming after them.
Important piece is the art-recovery specialist, as the third-party that bridges between the legal and criminal side. Gives a nice legal line item in the insurer's accounts.