They will not remove any copper lines. They will disconnect the drop cable coming from a pedestal or pole, at your NID (network interface device - the gray box). Your existing copper network in your home will be used.
Note that they will want to have a 110V outlet nearby, so they can plug in the new ONT (optical equivalent of your NID), and its battery back-up.
They should also be checking your coax cable in your house, to make sure it is good enough.
Make sure he does the "customer education" thing...rumor has it that some contract installers "forget" to do this.

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It is a truism that almost any sect, cult, or religion will legislate its creed into law if it acquires the political power to do so. Robert A. Heinlein


09 Jetta TDI
1985 300D