A function in which the input is needed for the computation is very different to one where it's not needed. I would expect the type signature to reflect this, why would you want it otherwise?
Or you have a function which expects objects of type String as an input. But then you realize that in your case, null values can be handled just like empty strings. So the input type can be relaxed to String|Null.
Just "" != Nothing
If you want to handle empty strings as a input in haskell then you have a function of type `f :: String -> b` and you pattern match on your input?
f "" = someResult
f ...