You can read section 3.3 on the general conditions of carriage for CX below
https://www.cathaypacific.com/conten...baggage-en.pdf
At most you may be able to negotiate for the fare difference for you original ticket and the price of a one-way ticket from NRT/HND to HKG but they have no obligation to actually honor this request.
Worst case scenario is you will need to buy a new one-way ticket back. If your schedule change was caused by something that is covered by travel insurance you have (if any), that will be the only way to claim back any money that is lost by missing your original ticket.