I have 10 months left on my 13-month lease. I don't want to sublease to anyone because then I would have to worry about whether they will make the rent, and if they don't, I believe I am responsible for making the payments. Isn't there something like assuming a lease whereby I pass all financial responsibility to the assumer of the lease and I am free to go?
You can get partially off the hook, but the barb will still be awfully close to your lips.
You can pawn off your lease -- or assign it to another person -- and thereby avoid being responsible for any damage for which the assignee fails to pay. But you will still be responsible for any unpaid rent, unless you get your landlord to expressly relieve you of that possibility.
To ensure this particular scot-free state, you'll need to secure what the law so often requires: a piece of paper. The one you're after is a Consent to Assignment of Lease.
This Consent need not contain any pseudo-legalese such as herein or wherefore. It can be as informal as a note, but at a minimum, should identify the landlord, the current tenant -- that would be you -- and the assignee. It should also include the address of the leased premises, the term of the lease you wish to assign, and a statement that your responsibilities to pay future rent and damages end, and that you give up your right to occupy the place. The landlord, assignee, and you must all sign the statement.
All this would happen if the world were utopian. But don't be surprised if your real life landlord refuses to put his or her name on the dotted line. Why? Your landlord may understand the consequence of such a waiver -- he'll lose a guarantor.