The Procession plays Encampment for the first time. You don't reveal a Plunder or Gold, so you set Encampment aside. This does not prevent Procession from playing it a second time, but both Encampment's attempt to set itself aside again, and Procession's attempt to trash it, will fail because it's not currently in play. You gain an Action card costing $3 ($1 more than Encampment), then at the end of your turn you return Encampment to its pile.
Reasons for what happens:
Procession needs to wait for Encampment to finish being played twice before it can do the trashing. It can't find Encampment if it's set aside (because it has "lost track"), so it can't trash it.
Procession's "gain an Action card" effect does not depend on successfully trashing the played card (as noted in the FAQ).
"Lose track" effects only happen when an effect tries to move a card, but the card is in an unexpected location. So Procession "thinks" the Encampment is in play and tries to move it to the trash, but since it's not in the "in-play area" it can't trash it. But being set aside doesn't change Encampment's text or cost so it still does the same thing when it gets played again, and it can still be used to calculate the cost of the card gained by Possession.