When Exhausting is listed as a Cost, then the Action must be able to be completed for the cost to be paid. Example: A spell says "As an additional cost to play this, you may exhaust a friendly unit." An exhausted friendly unit may not be exhausted again as the additional cost for the spell, and the additional cost has not been paid.
§ 414.4 Core Rules PDF (officieel)
§ 414 Exhaust
