Vague and hypothetical, but does anyone have a general rule of thumb as to if/when the IRS will exercise its right of redemption on a foreclosed property?

Case in point: Property purchased at mortgage foreclosure auction. Former owner owes over 100K in taxes, property has a tax lien. IRS has 120 days to redeem, pay off winning bidder, and then sell to recoup. Question is... when will they? Obviously the amount of the lien plays a role (bigger the lien more likely they will, I would assume). 

That small print will get ya!