Do the TPG's return labels after crossovers?

For example: If an NGC coin is sent to PCGS and is crossed, does PCGS send the label back to NGC? Does NGC do likewise?
Buyer and seller of vintage coin boards!

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I would suspect that the majority of crack out labels never made it back to the TPG's.
Because of this, pop reports are skewed to the point of pure inaccuracy.
Most rare coins are MUCH rarer than the pops suggest, so I don't even follow them much anymore.
Sometimes, it’s better to be LUCKY than good. 🍀 🍺👍
My Full Walker Registry Set (1916-1947):
https://www.ngccoin.com/registry/competitive-sets/16292/
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