Can a landlord keep your security deposit if you never signed a lease or moved in?

In Massachusetts, the security deposit may lawfully be applied toward damages to the unit or unpaid rent.  There are very specific requirements for taking and retaining security deposit payments.  Talk to a lawyer.  You will want to send a demand letter and, if you do not get a reasonable response, you will want to file in small claims court.  A court may award triple your security deposit and attorney's fees if your landlord is in violation of the security deposit law.  Good luck.

No.  The security deposit is solely for "damage" in residential tenancies in Rhode Island.  Individual circumstances in each case do have an influence on the outcome, but I can imagine no case in which a landlord would be able to retain the security deposit if you caused no damage or didn't move in.