If your tenant wants to move out in the middle of her lease. normally she may not do this. She signed the lease, so she is bound by it, just as you are. She cannot simply "break" a lease.
What if the landlord breached the lease?
If you breached your express or implied promises in the lease in some significant way (e.g., by failing to keep the place habitable), she may have the right to terminate the agreement before it expires. She has been "constructively evicted," so she may end her obligations under the lease.
May the tenant find someone else to take her place?
If the lease has no language preventing her from assigning or subleasing, she might try to find someone else to take your place. This person will pay rent to her, and she will pay it to the landlord. If this person fails to pay the tenant, the tenant still owes the rent to you - unless you accepted this new person as a replacement for the tenant. You have no obligation to accept the new person as a replacement (i.e., one that gets the old tenant off the hook) - though you may have to accept the new person as an "assignee" or "subtenant." This might not be bad for you, as it might give you two sources for the rent: the new person and - if he fails to pay - the old tenant.
Sometimes your agreement will allow the tenant to assign or sublease, but only with the landlord's consent. If the tenant presents a potential assignee or subtenant to you who is a good tenant, you might be breaching the lease if you unreasonably withhold your consent. This might constitute a "constructive eviction" that allows the tenant to terminate the lease.
What if the tenant simply moves out?
If the tenant simply moves out during the lease, she has breached the lease, and you may hold her liable for your damages. You might sue her or simply take your losses from the security deposit. But in most states you have a duty to try to "mitigate" your losses by renting the place as soon as possible to someone else. Even if you are able to re-rent it quickly, you still might hold the tenant liable for advertising costs and the like.
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