Return donations to members

My stake is participating in a multi-stake convention out of town. Some YSA have made partial payments to fund their attendance to the activity. What is the procedure in case one YSA does not or cannot attend the convention for whatever reason? If the member requests the ward to return the money because they did not attend the activity, what should be done? Can the ward return money in such situation?

The money for this kind of event should be place in a sub-category of the Other:Authorized Member Financed Activities category. Refunding money to a donor from such a category is allowed and even required if the money will not be used for the purpose it was donated. See the second full paragraph in the Help Center article The "Other" Category.

This isn't a donation, so, if the situation warrants, it can be returned. However, that depends on the details. If there's left over money, or the event organizers can make a full or partial refund, then yes, it should be refunded. But the ward is under no obligation to be out of pocket. It's possible that the cancellation came too late to avoid the expense. In that case, the YSA got a life lesson.