Fibre is a brand new line into your home which rules the copper line redundant. The fibre optic cables that are installed are more resilient, less susceptible to weather-related deterioration and providers a much better service.
Once fibre is installed, you'll have no need for the existing copper cabling. There's a good chance the local fibre company will completely disconnect it too. If your landline phone requires power, it will continue to work. Old-school phones that take power from the copper line (i.e don't plug into the power outlet) won't work over fibre.
If you have a medical alarm or security system that requires a phoneline, it should continue to work over fibre. Your local fibre provider will connect your existing internal wiring to the ONT, ensuring your current jack-points, or any hardwired devices, continue to work.
Regardless, we'd recommend checking with your monitored alarm provider and ensuring their equipment is fibre ready. Feel free to get in touch with NOW too.