Here are the T&C for the airline.
http://www.cathaypacific.com/content...baggage-en.pdf
They do not specifically address your situation, but do indicate the airline is willing to deal reasonably with passengers' illnesses.
3.1.4 If you have a Ticket, as described in 3.1.3 above, which is completely unused, and you are prevented from travelling due to Force Majeure, provided that you promptly advise us and furnish evidence of such Force Majeure, we will provide you with a credit of the non-refundable amount of the fare, for future travel on us, subject to deduction of a reasonable administration fee
3.2.3 If after having commenced your journey, you are prevented from travelling within the period of validity of the Ticket by reason of illness, we may extend the period of validity of your Ticket until the date when you become fit to travel or until our first flight after such date, from the point where the journey is resumed on which space is available in the class of service for which the fare has been paid. Such illness must be attested to by a medical certificate. When the flight coupons remaining in the Ticket, or in the case of an Electronic Ticket, the Electronic Coupon, involve one or more Stopovers, the validity of such Ticket may be extended for not more than three months from the date shown on such certificate. In such circumstances, we will similarly extend the period of validity of Tickets of other members of your immediate family accompanying you