Got a cell phone service/security question.

I lost my cell phone Sat. Sun, I suspended the service and reported the
loss. The cs rep I talked to said no activity had taken place through my
number during the window from when I lost the phone 'til when I reported it.

I will eventually get a replacement cell phone, and plan on reusing my old
number.

The question I have (this is where it gets dicey; I've asked this of the
cell service cs rep already. His reponse was not meaningful. We talked in
circles. I don' think he ever really understood what I was asking) is:

a. Once I get my replacement cell phone, and....

b. Have service under my old # reactivated.....

If someone comes into posession of my old phone, could he/she also use my
account when I'm also using it with my new phone?

It seems to me that there would have to be some unique characteristic of all
cell phones that enable the terminal eqpt to distinguish between them to
prevent such a thing. The cs reps I've talked to can't tell me this is the
case. They just keep repeating the mantra : with your new phone, you're
the only one who can use the account.

I don't get a warm fuzzy feeling about the capability of my cell service to
prevent someone out in the wild who recovers my lost phone from using it,
too, once I activate the same phone #.

Would appreciate words of wisdom on this concern.