Unless you have a clause allowing them to change their mind & back out within a prescribed period of time, at the very least, they should forfeit the money they already paid you, and might very well be liable for any other losses you incur..
How much time has elapsed from the signing to their change of heart?
If you used an agent you should discuss this with them...if you didn't, i would push back, but you might need to consult an attorney at some point if the "tenant" gets nasty.
A lease is a legally binding contract (which is something many renters don't seem to understand). You might want to negotiate liquidated damages - perhaps two months rent - which would cover the time you spent looking for a new tenant.