Although this has never happend to me and I have never bought such a battery off of ebay, I thought I might as well tell you about what may happen from cheap batteries purchased from other countries.
This problem generally only concerns newer Lithium ion or li-ion batteries. These battries will explode if they are overcharged, and therefore do not like being kept at maximum charge for an extended period of time. The simple fact is that these batteries will explode. To prevent this from happening in commercial products, the batteries incorporate circuitry which will prevent the battery from charging further, or at the least the device will stop the battery from charging itself.
This problem has been highlighted with the recent Apple battery recall. These batteries are manufactured by Sony and if they can get it wrong then what do you think of your cheap battery will do? Unless you are sure they offer the same protection mechanisms then do not buy them, you are not just putting your device at risk but you own safety.
The other issues to concider on the whole is that they will most likely use a thinner casing and will be prone to leakage.
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