THIS IS NOT LEGAL ADVISE - I AM NOT A LAWYER. This post is for information purposes only. You should obtain a lawyer if you have legal questions.
I will only talk about contracts generally, and your situation has certain specifics that could change the way an issue is handled.
In contracts, if you breach, the nonbreaching party has a duty to mitigate damages. In other words, they must attempt to relay the contract onto the market. So if someone just walks away from a lease, they are breaching a contract. Usually landlord gets the difference between the new renters rent rate and your previous rate, plus whatever costs to advertise/put the thing back on the market. (if its vacant, i guess they would get the whole months/length to reoccupy rent)If you find someone to take the lease, that is basically a cost averted, so you would have to pay the difference, if any, between the rates (because landlord suffered a loss of value with a lower rate over the next 9 months than he would have had if you performed the contract). But then again, some places have qualifications for renters, and the new renter must also meet those. When someone takes a lease it is an assignment, and the contracts usually say you must obtain permission from the lessor/landlord.
Another concept is liquidated damages. Liquidated damages are basically damages that parties contract for in the event of breach, so for example, your cell phone bill says you must pay $150 to cancel your phone plan, that is a liquidated damages clause. These types of damages are ok where they are not punitive, or made to punish, because public policy does not want people deterred from making contracts where they could be hit with huge damages that might exceed what they originally contracted for. So if Sprint wanted a couple thousand to cancel my phone plan, that would probably be an unenforceable liquidated damages clause.
So if someone who is leasing wants to leave and finds someone else, the new lessee would fill out an application just like everyone else who applied to live there, and once qualified would take over the payments. If not qualified, they have to know why.