Made an application, paid application fee, left a check to pay security deposit WHEN they came to sign a lease. They have changed their mind, don't want to lease there anymore but apt complex says they are obligated to leave their security deposit because they reserved a unit for them. The agreement was that the check for security deposit would not be deposited until lease was signed. Are they obligated to leave their security deposit now and/or lease from that complex? Or can they move on to somewhere else?

They are not obligated to the lease, since it was not signed.

They are obligated to any terms of the application, what did it say about the deposit. Next why did you leave one ? Was it a requirement, if so what was the rules on it you were given