I'm not sure the Borg have ever demonstrated the ability to fight with fragments of a ship, or even with a seriously damaged ship. A swarm of Cubes will probably operate like a swarm of Drones, with individual units taking great risks because even their destruction will be to the advantage of the Collective. But individual ships have been disabled and negated as threats in many episodes, starting with "Q Who?", until time-consuming repairs could be effected - and extensive damage has resulted in infinitely long repair times, such as with "Unity".
"Our projections indicate that a Borg ship could continue to function effectively even if seventy eight percent of it was inoperable."