Will my IPhone enter lost mode after a stranger resets it?

It is not possible for anyone to factory reset the phone unless they know the passcode, Apple ID and Password associated with the phone.

If you enabled Find My on the phone.....before......it was stolen and "Offline" is appearing when you try to locate the phone, this indicates that one or more of the following conditions is true:

• The battery has run down
• The phone has been powered off (most models)
• The phone does not have an Internet connection where it is located
• The phone is working fine, but the thief has placed it in a special type of small bag that will not allow the phone to send or receive a signal. (Unfortunately, this method is very popular among the bad guys)

If the phone comes back "Online", it will accept your request to enter Lost Mode.

Not what you want to hear, but you have to be realistic. Only a tiny tiny fraction of stolen phones are ever recovered. These are the phones left at a restaurant with honest employees or a shop with the same type of people.

Even if the phone's location appears, you would probably never want to try to retrieve the phone by yourself, and the police will likely not help.