Is there a law in Arkansas against searching employees cars as they leave the company premises to check for stolen items?
The legality of the matter may be secondary to whether you wish to remain employed or not. Arkansas is a 'right-to-work' state - which means that (except for certain industries) you can be hired or fired at the whim of your employer. If part of your employment is being subject to unannounced searches of your lockers, and automobiles (while on company property) I would tread carefully if I were you.
Some rights that landlords have against tenants include the right to enter to premises for inspection and in case of emergencies and control of the premises, such as to make repairs, installing signs and performing other maintenance. Other landlord rights will vary depending on the contract you sign.