一般来说，如果去打官司，法庭赔偿房东——受损失一方时，会尽量依照这么一个原则：使房东得到跟合同履行时相同的租金——“to place the injured party in the position it would have been in had the contract been performed”。
当然，这里还涉及到duty to mitigate damages——受损失的一方即房东有责任在可能的范围内最小化其损失，比如在这里，你的房东很快去找了新的租客，她做到了她该做的。新的租金少于旧租金的那一部分损失由你负担是正当的要求。如果她尽力去找了新房客，但是很不幸一直找不到，她要求你赔偿全部的租金也是合理的。
关于你想继续住下去，不搬走来避免赔偿，似乎也不是如你所想象的那样。当你宣布不履约的时候，你的房东有权力把你们的合同视为discharged。这是由她来选择的。如果她这样选择，你如果要继续住下去，必须跟她签订新的合同，因为你们的旧合同已经不存在了。从你叙述的情况来看，你的房东把房子重新offer出去了，并且被别人accept了，当他们正式签订合同，你会被要求搬走。
所以，签约和违约的时候，尽量三思而后行。事后再来责备房东黑心，似乎缺乏法律的依据，也许你能得到一些同情，但是，我建议你理智一点。
一家之言，仅供参考。

如果怕房东捣鬼, 用UPS,给他把收据留好.
你的DEPOSITE 可能没有了, 但是让你付损失是不行的. 去查一个"居民用房出租条列"之内的东东(帮助移民的协会什么的因该有), 凡是超出上面的要求一概拒绝.

我的合同签了2年, 一年就搬出来了, 房东(香港人)挺客气,连DEPOSITE都全退了.

本文发表在 rolia.net 枫下论坛End of tenancy agreement
32 (1) A tenancy agreement is ended only

(a) if a notice of the end of the tenancy agreement is given in accordance with this Act,

(b) if the tenant has vacated or abandoned the residential premises,

(c) on the effective date of an order for possession of the residential premises in favour of the landlord,

(d) on the date specified by a court under section 37,

(e) if the tenant has elected under section 83 (3) to treat the agreement as ended,

(f) if it is a fixed term tenancy agreement described in section 9 (2) or (3) and its term has expired, or

(g) if, after the tenancy agreement is entered into, the landlord and tenant agree in writing that it is ended.

(2) Subsection (3) applies to a landlord if

(a) an agreement under subsection (1) (g) is made respecting a manufactured home pad in circumstances other than where the tenant is renting a manufactured home and the manufactured home pad under a single tenancy agreement, and

(b) the landlord does not advise the tenant of the tenant's rights under section 38 (11) or 40 (3) before entering into the agreement.

(3) In the circumstances referred to in subsection (2), on the end of a tenancy agreement under subsection (1) (g), the landlord must pay to the tenant the amount of the tenant's actual and reasonable moving expenses, up to a maximum prescribed amount, without delay, after

(a) the tenant vacates the premises, and

(b) the landlord receives a written account of those expenses.

(4) Despite subsection (1), a landlord must not regain possession of residential premises unless

(a) the tenant has vacated or abandoned the premises, or

(b) the landlord is acting under the authority of a writ of possession.更多精彩文章及讨论，请光临枫下论坛 rolia.net