The physician prescribing the isionizaid should be ordering regular blood tests to check for liver injury. If the tests show evidence of this, then they would stop the isoniazid, unless the tests are borderline or show only minor injury, in which case they may decide to continue but increase the frequency of tests, to ensure that it doesn't deteriorate.
Many people do get some abnormality in the tests, but once the isoniazid is stopped, the liver recovers over a period of a few weeks to months. The liver has very powerful regeneration capability, so it can recover after a significant injury - the only catch is that a low grade injury that is carried on for many years (e.g. alcoholism) will cause the liver to be scarred and fail (cirrhosis, hepatitis B). 9 months shouldn't be enough for this - this really does require many, many years.
Very rarely (I think it's about 1 in 20000 or so), some people develop severe liver damage as a result of isoniazid - the reason why isn't known, and it doesn't appear to be a normal toxic response (as it can cause severe injury even at small dose), it appears to be unpredictable, but specific to the person.
A final note, a positive PPD doesn't mean you have TB - it means that you may have been exposed previously. I must confess, working in the UK, that I've never heard of treating someone for a positive PPD before - over here, you only get treated if the chest x-ray is positive. However, you should follow the advice of your local physician, as variations in regional guidelines exist for a reason.
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