When Recycling is listed as a Cost, the action must be able to be completed for the cost to be paid. Example: Vi, Destructive has the ability "Recycle 1 from your trash: Give me +1 [M] this turn." Each time a player activates the ability, they must recycle 1 card from their trash to pay its cost. If they have no cards in their trash, they can't activate the ability, because they can't pay its cost.
§ 416.3 Core Rules PDF (officieel)
§ 416 Recycle