Breaking a renter's lease can bring on a legal battle and credit damage if a judge places a judgment on your credit report. Broken leases breach a contract between you and your landlord. Understandably, losing your job or going through a break-up can hinder the ability to afford your apartment. Instead of moving out and risking credit damage, see if your landlord will release your rental obligation without penalty.
Familiarize yourself with the rental agreement to see if economic hardship constitutes breaking a lease without penalty. If so, the landlord might dissolve the agreement following a job termination, if you can provide proof of this (letter from employer). What's more, the lease may grant early dissolution if you relocate for the military or employment.
Compensate the landlord financially. Losing money is likely your landlord's biggest concern. Ease his concern by agreeing to buyout the lease. Pay for the months remaining on your lease and then vacate without penalty. Get this agreement on paper to prevent any future legal battles.
Offer solutions if you don't have cash to buy out the lease. Not everyone has disposable money to write a lump sum to pay off a lease. Present your landlord with other plausible solutions. For example, submit a written notice and propose that your landlord allow early termination if you provide rental payments up until they find a new leaseholder.
Rent out the unit yourself to avoid penalties. Since you're responsible for rental payments until your lease ends, locate someone to occupy your unit and charge this person rent. Write a check each month and submit payments to your landlord as usual.