What happened to the faucet?
The person asking the question wants s to know what has caused a sudden change to the faucet (recent or not), because the faucet is not in the same way as expected. May be the faucet is removed, unattached or was destroyed by some external event. Something happened from outside of the faucet and created a change.
What happened with the faucet? The person is either surprised or objects to the fact the faucet not properly working or a physical change that’s more from within the faucet.
Say I come into kitchen and see the water spigot is running and I try to turn off the faucet but it fails to shut off. So I ask, what happened with faucet?
Or I was expecting a new faucet to be arriving by order, but it never came. I call the company I ordered it and ask: what happened with the faucet I ordered? It hasn’t arrived yet.
So think of these two question from different angles around the indirect object, the faucet.