When the City sells a lien, it is not selling the property. The lienholder does not take title to the property. The lienholder purchases the right to collect the money that was owed to the City. Ultimately, however, if the property owner does not pay what is owed, the lienholder can begin a formal foreclosure proceeding in court.
Once a lien is sold, the property owner then owes the taxes, charges, and accrued interest to the new lienholder, not to the City. The amount the property owner owes automatically increases once the lien is sold, because the lienholder is entitled to receive a 5% surcharge on the entire lien amount, plus 18% interest, compounded daily and payable semi-annually. The property owner may also be responsible for paying other administrative costs associated with the lien sale; for example, legal and advertising fees.
I've been digging around researching property tax liens as well, although my searches have focused primarily outside of NYC.
As you probably already know, the availability of property tax lien certificates (and the laws governing them) vary widely by state and county.
If you haven't already done so, I would recommend picking up a copy of "The 16% Solution" (make sure you get the updated version), and reading it carefully. It's not exhaustive, but it has quite a lot of useful information and resources.
Toilet seats that serve as Bidet Attachment to Bidet under seat mounting types can be used.
Hope that helps!