Were they placing earnest money down to purchase your rental property, or were they putting a holding deposit down so you would take it off the market and allow them to rent from you? I'm guessing you're referring to the latter scenario.
When you agree to rent to someone, they are under no obligation unless you have something in writing. It sounds as if you agreed to rent to them as long as they put some "earnest money" down, which they did. But if there's nothing in writing that contractually binds them to renting, they can back out at any time.
Any time a potential tenant wants to rent from me, I require money down and a signed holding contract. My holding contract states I will take the unit off the market and hold it for them (never more than seven days). If they change their mind, the holding deposit is used to pay for the number of days the unit is vacant until a suitable replacement tenant is moved in. If they decide to rent from me, the holding deposit converts to a security deposit once they sign the contract. The key is to get everything in writing. If you take people at their word, you'll soon learn that words are cheap.