When a contract is agreed to and signed by all parties, for lease or sale, the home goes into a "pending" status per the local Realtor MLS rules. The home is still on the market for lease or sale, but the signed contract is in control and no other renter/buyers can bump the first party out of the way. Real world, most renters/buyers will see that pending status and move on to other properties.
If the "fee" your speaking about is a deposit, the return of the deposit depends upon the wording in the lease. If the landlord wants some small fee from you while your working out the lease terms may be reasonable, but make sure it is addressed in the lease and how you can get these funds back.
Best advise.... Work with a Realtor, even on leases!!
Bernstein Realty, Inc.
If you app is not approved, the deposit should be refunded.
If the application is approved, then typically the deposit would not be refunded until you complete the lease and return the house in the same condition and complete all other terms of your lease.