I realize this is an old discussion but thought I could add some information.
We also receive donations to the Ward Mission Fund that are not designated for a particular missionary. The fund builds up over time to a fair amount of money. About three years ago, we got a notice from our Area Authority Seventy that there was too much money there and it needed to be transferred to the Stake promptly. The rules were that we could retain any money that was paid in advance for an individual missionary and enough money to cover our missionaries for three months in the event something changed with the family finances. This has become an annual event and I am expecting a letter any day now asking for the money.
As I understand it, the stake has the option of distributing the funds to another ward if there is a need. Otherwise it is sent on the Church General Missionary Fund.
Now, here is where I might run into some controversy. I would be very hesitant to deny the blessings of supporting a missionary to any family. If they can meet the obligation and are willing to do so, I'm not taking that opportunity away from them. I would much rather see the money go to another ward or area where there is a true need.
These are just my experiences and opinions. Ultimately, this is a discussion that takes place between the bishop and stake president.