I try to make it a habit to always go to the icloud.com website in my browser without following a link, but it’s easy to forget when you’re worried about a lost phone.
I actually recovered a lost phone like this. First, there is a setting in find my iPhone (in the iCloud settings) that lets you turn on “Send Last Location”, which helps finds phones that have been shut off. Second, I had a criminal call the number I put into the phone. He told me he “found” the phone and he’d like a reward.
It was my company’s phone, so our asset protection group actually handled dealing with the police to get the phone, but eventually, I got my phone back in a plastic bag.