The date of departure should be agreed by the Yan-Yan, as she has the right to stay in HK for 14 days after contract termination, to look for new job. If you fix a day without asking
her and if she wants to 'play thing', she could refuse to accept your ticket and you have to change the date for her (may incur cost).
If she agrees a day and wants to change it after air-ticket is issued, it is her own effort / expense to do so, not your responsibility.
If due to some reasons that you do not want to ask for her date, a possible way is to set it to be the last day (14th day) of her stay after termination (eg. fired on 31-Mar, last day in HK
is 14-Apr), and they would usually accept that.
If she misses the flight, it is her problem and you have no responsibility to solve her problem.
Don't worry about the date too much. They will try to get a new job in the 14 days, and if they could not, some agencies will
- help them to sell away the air ticket (money goes to the ticket holder, the Yan-yan, not you),
- send her over to China / Macau after 14th day to meet the Immgration dept requirements of leaving HK,
- then come back to HK as visitor for 30 days of stay, to keep looking for new job.
If they still could not find a new job in the 30 days, they will repeat the move and come back to HK for another 30 days of stay -- two stays in max before returning to home country.
I learnt about the air ticket arrangement and agent's trick from the friends, before firing my Yan-yan. To 'rescue' other families from the possible torture of hiring such bad maid, suggest you to post your bad Yan-yan's names to the blacklist to alert others.