You can decline the leave, certainly. And if the individual then goes off sick during that period, you can ask for appropriate evidence to be provided. The employee is completely in the wrong here, and if they lose a deposit on the holiday, then it's their own stupid fault.
However, if I were the manager in this situation, I would be considering whether the employee in question was generally a good worker or just a piss-taker in general. If a piss-taker, then I would not hesitate to decline the request, but if he/she was generally a good employee and this was just a one-off stupid mistake, I would consider long and hard whether there might be some way of accommodating the request without detriment to other staff. I would certainly make it very clear that the employee should have asked first, but if I could somehow find a way of working around it for a good member of staff, I would.
In fact, that's exactly what I did for one employee a few years ago, who had stupidly booked without checking (she had assumed that the time in question would be ok) and had paid for the entire holiday already. She fully recognised that she had been wrong to book without asking, and really appreciated the fact that we managed to find a way of working around it. It was very inconvenient at the time, but that employee will now go over and above in order to be flexible when we need her to be, and to help cover leave for other colleagues. In my experience, a little goodwill in the workplace goes a very long way.