Can I sign an sublet agreement with a person who did not qualify through the leasing office?

The answer lies within your lease. Most leases, especially apartment leases, will have provisions specifically dealing with "subletting." These clauses usually put restrictions on who you can sublet to and whether or not it needs their approval. Whether or not your end around their normal approval process will work will ultimately depend on the terms of your lease. Hire an attorney on a project basis to take a look at it and give you specific targeted advice. Best of luck!

I agree with Mr. Conticello. But why would you want to trust someone who could not pass the leasing application? Does that not give you pause as to what kind of subtenant you will have?