A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
http://imperialassembly.com/oracle/#cardid=10540
Void Limited, w: Reduce a Province's strength to 0. If its player has two or more Provinces, you may remove five Koan cards you control from the game to destroy it.
Is the bolded part considered a 'cost'? If not, and if somehow one of the cards isn't removed from the game, is the province still nuked?
Is the bolded part considered a 'cost'?
No. HOWEVER, quoting from the CoM rulesheet:
6. Some effects are phrased conditionally, for example, “he may bow one of his Rings to draw a card.” This means that the player may bow one of his Rings; if he does so, he draws a card. The bowing in this example is not a cost, but if it fails, the effect “draw a card” does not happen.
If not, and if somehow one of the cards isn't removed from the game, is the province still nuked?
If you fail to produce the effect before the "to", the effect described after the "to" will not happen. Treat the clause preceding the "to" as a required condition for the clause following it.
In your example, failing to remove five Koan cards you control from the game would cause the following effect (destroying a province) to not happen.