optional closure and check if it is nil

You need to wrap your closure signature in parentheses to make the closure itself optional. The way it’s written now, the closure returns an optional Void (which doesn’t really make sense).

var completionHandler: ((sucsess:Bool!, items:[AnyObject]!)->())?

Some style points and revisions to your example code:

 // Capitalize class names so it's clear what's a class 
class SomeClass {
    // "success" has two "c"s
    var completionHandler: ((success:Bool!, items:[AnyObject]!)->())?
    var hitpoints = 100
    var someset = ["oh no!","avenge me!"]

    init() { }

    func getHitFunc(impact:Int, passedCompletionsHandler:(success:Bool!, items:[AnyObject]!)->()){
        completionHandler = passedCompletionsHandler
        hitpoints = hitpoints - impact
    }

    // You were missing the argument list here:
    func checkIfDead() {
        if hitpoints <= 0 {

            // Rather than checking to see if the completion handler exists, you can
            // just call it using optional syntax like this:
            completionHandler?(success: true, items: someset)
        }
        completionHandler = nil
    }
}