There's no precedent for that in the United States, but worldwide there are different types of referenda. The situation you've described is quite rare, that you enact the change and then ask for a vote later. What's more common is that you would have an advisory referendum. First you say that you're going to put this out to a vote, but we're not going to implement it yet and it's not going to count; we just want to get a sense of the people. That's a little more common as an alternative to the normal referenda where you vote on it and they implement it.
The case that you've described happens, but it's pretty rare. Once governments invest in a change like this, typically there's a reticence to put it out there and change it. It has happened, but it's really rare.