Name for type of actions that only care for outcome There is a definition for kind of actions that only care for outcome.
Classic example for such an action is remove from collection:
When you try to remove an item that doesn't exist in collection, there are two possible outcomes: failure with item doesn't exist or success (because the outcome is that the item doesn't exist).
I'm interested in the second one. 
How do you call remove that succeeds when the item it is trying to remove is not present?
This doesn't actually answer the question but it fits to be an answer.
What I looked for is idempotent (when I asked this question I was actually looking for this word, but failed to express myself properly). 
The definition is quite different from the question asked here: 


  In computing, an idempotent operation is one that has no additional
  effect if it is called more than once with the same input parameters.
  For example, removing an item from a set can be considered an
  idempotent operation on the set.


But indeed, any operation that is idempotent will meet the question criteria.