Never say never...
SIP Trunk - The level headed choice
It is possible yes, but as previously mentioned by mfinni it is dependent on your provider and your internal set up.
If you have the PRI for an interal PBX for example, you could have the traffic re-delivered over the fibre if your provider supports SIP trunks. Your PBX would need to support SIP trunks and the fibre provider would need to be the same provider as the existing PRI (in this theoretical scenario) so they can route the same numbers to you down a SIP trunk.
If not you are going to need a number porting agreement between providers and then, well, it really is getting to specific to talk about here.
So to wrap up, if its the same provider and they are any good, this is perfectly possible.
Encapsulation - The long shot
Since you are having a fiber line delivered, presumably a new shiny CPE will be heading your way too. If you have an MPLS capable device and your provider supports (this isn't very common) you could have the PRI data delivered to you as "Circuit Emulation over MPLS" (AToM) whereby an MPLS Pseudo-wire emulates a TDM link.