Apple does nothing in terms of monitoring or searching for your device. They will never contact you about it since they have no knowledge it is missing and are not tracking it or trying to. Apple does not get involved with lost or stolen personal property at all.
The only way to track it is for you to regularly check find my iphone yourself.
If you receive any unsolicted message saying it is found - text, email, call, etc - it is nothing more than a phishing scam trying to get you to compromise your information such as AppleID password.
If you do use lost mode to put a message with contact information on the lock screen, be very careful of what you put there, and what you respond to if someone uses that information to contact you. In particular, never give out your AppleID password to anyone. Apple, by strict privacy policy, will never ask you for it, ever.
https://support.apple.com/en-us/HT201472 note the part about:
"Find My iPhone is the only way that you can track or locate a lost or missing device. If Find My iPhone isn't enabled on your device before it goes missing, there is no other Apple service that can find, track, or otherwise flag your device for you."
