What if you're looking up the input in a temporary cache of some kind, and returning a reference to the cached value? The lifetime of the input and output would not be related in that scenario, but the output would not necessarily be 'static (maybe you build a cache, run some functions, tear it all down, then build a new cache with different values and do it all again).
(Or when it has a lifetime of `static`, which means the referent is stored in static memory and thus is alive for the whole program.)