In one of my local systems there is independent faction A owning 2 stations, empire faction B owning one and federation faction C owning one. A civil war pending between A and B occurred when faction B reached the same influence % (14 in this case) as A. By the time the war started, B had already passed A and gone to 16%. During the civil war neither factions influence changed, as expected. Handing in combat bonds at 3k per ship during a civil war makes very little difference, as opposed to a high profit trading runs at the stations during peace. Faction C, meanwhile, benefited from trade and crept up to 14%.
So eventually the war ended. Local Galnet said both factions had "won", with faction A holding on to one of it's stations (where there had been no conflict zone nearby) and faction B holding onto it's one station (where also there had been no conflict zone nearby - there were two zones by faction C's station, so conflict zones don't tell you which stations you're fighting for).
Now factions A (14%) and B (16%) are at Civil War pending, which seems odd since faction C is at 14% now. If it worked the same way as before you'd think A and C would fight, but IIRC there was some talk about the change in influence being important, not just the current level - which would imply if two factions are of similar % and don't change much, they tend to end up in constant battle, while the other factions make hay and boost their influence through trade.