For adventure mode I can place items created with CanPlaceOn and then use other items to pick them up using CanDestroy, however when the destroyed item is retrieved it no longer has any nbt data it was given, including the CanPlaceOn tag so it can't be placed again.

To reproduce I use these commands to give myself a bed that I can place in adventure mode, and an axe I can use to break and retrieve the bed:

give @p brown_bed{CanPlaceOn:["grass_block"]}
give @p iron_axe{CanDestroy:["brown_bed"]}

But after retrieving the brown_bed it can no longer be placed again.