I have recently been through this process using BT contractors (ie its BT broadband being installed)
In my experience no they do not remove the old line. In my case they don't even come off the same pole. Old analogue line is off pole at front of house, new fibre is off pole at back of house. They would not go round to where the old line entered the house "as the fibre cable wont bend round the corners of the house". Its minimum bend radius is quite large.
Your current master socket will be redundant. A new one will be installed (a modem) which has to be close to a power point as it will need mains power. And in my case they insisted that it must be on an outside wall.
OpenReach have previously moved the Master socket from where it enters the property to the new location and put connectors (in the old box) and used my cat6 cable to do it.
In my case they were very keen to install the modem on the ground floor
- but the wall where they wanted to put it luckily had no power. (the fibre termination box has to be at ground level for future serviceability - to save climbing ladders to get to the cable terminator)
So they brought the fibre from the pole to the eaves of the house and down the outside wall to a termination block, then from the fibre termination block a cable goes back up the wall and through the wall on the first floor to the modem (which connects to the router).
My fitter was adamant that the modem must be fitted on an outside wall. (you can then put the router wherever you like if you have a suitable network cable).
(Make sure you put some carpet dust protector where they will drill the hole in the wall).