If I target a kensai with The Laws Strength, then react with Improper Papers at the correct time, is it already too late for the player to react with Hundred Fold Cut to negate the kensai's destruction?
The Laws Strength and Improper Papers vs Hundred Fold Cut
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.
If I target a kensai with The Laws Strength, then react with Improper Papers at the correct time, is it already too late for the player to react with Hundred Fold Cut to negate the kensai's destruction?
This is correct. Hundred-Fold Cut reacts after targeting; Improper Papers reacts before an action's resolution.
In tournament play, you will need to give your opponent an explicit opportunity to play Hundred-Fold Cut. I've seen lots of players just throw down Law's Strength and Improper Papers together; your opponent must pass their opportunity to react to targeting before anyone gets the opportunity to react to movement.