The function (even a closure) would be fully recreated on deserialization, it is fully safe to save it to disk. It wouldn't preserve reference equality -- it would be a new function -- but the behaviour and the state (if using closures) would be equivalent.

I didn't include asserts in the linked case, because I thought it would be too verbose. You can see asserts in the test, that is linked below the example. Maybe it was the wrong call, I will think about including asserts into the example itself.