Using the assumption, you gave a signed lease with a security check to the rental agents. You have only made an offer to rent at a set price and conditions. The check is added to show your serious intent and to allow the lease contract to be both accepted and made active simultaneously. You've only submitted a package to the agent, in order to be presented to the landlord for review. If your lease terms are accepted, you receive a copy of the lease with everyone's signatures. If rejected you receive either a counter offer, for you to review, or you just get your check back, so you can move onto looking elsewhere. Having multiple people interested, can mean multiple lease packages being presented to the landlord for review. They accept the one most to their liking and reject the others. Until you receive an acceptance, you have the option to keep looking and/or cancel the your offer, should you find something else or just simply don't want to wait past a certain time frame.