Blake,
Greetings from a fellow investor and attorney here in Elizabethtown. Did you pick up the property at the Hardin County master commissioner sale? If so, I was probably there as a good deal of my practice is real estate tax lien foreclosures and I am there most Wednesday's for the sale.
As for your question, I am very familiar with how the law views right of redemption in Kentucky as the majority of the properties my client gets at the MC sale is for less than the 2/3 appraisal value. I advise for the 6 month period to do the bare minimum to keep the city/county off your back on mowing, maintenance, etc., as the court's in Kentucky have interpreted the statute to mean what it says so any improvements beyond how you bought the property cannot be recovered if the owner decides to exercise their right to redeem.
In your question, let's say you bought the property for $20K and you begin rehab, cleaning it up and getting it into livable condition when it was not in that condition when you bought it and you spend another $20K doing that and/or you sweat equity with your work and one day before six months runs out the original owner decides to redeem they can pay $21K into the court and get the deed immediately back. You will receive your original purchase price of $20K back. You will then have a lien against the property for any expenses that you incurred and will have to hire an attorney like me to again foreclose and argue you should get your $20K back you spend on rehab which will likely be a losing argument since improvements have been held not to be expenses under the statute.
Be aware under (1) that it can be the defendant or "his or her representatives" can redeem. There are companies working here in Kentucky right now that monitor sales for less than 2/3 appraised value and then if someone like you begins rehab they approach the original owner and offer them $500.00 or so to assign the right of redemption and then the company pays the purchase price into the Court and get's your rehabbed property. This was recently ruled a valid action by the Kentucky Court of Appeals.
Be wary of the pitfalls of this and other things that can go wrong at the master commissioner sales. As I advise everyone who asks if you are going to spend tens of thousands of dollars on a property plus your valuable time getting it rehabbed the cost of getting an attorney on board at the start who knows real estate law and can address such issues is a drop in the bucket compared to making a mistake that costs thousands, tens of thousands or if you ever get into big developments, millions. I can't leave my contact info here but if you ever have any questions about real estate law or real estate in the area in general give me a call. My number is online and in the local phone books. Good luck. Thanks.