Thanks for the replys @Ned Carey and @Bruce Lynn! You've given me information to think about and chew on for a while.
For what it's worth, the property is in Clinton County Indiana. Tax sales are through a contracted agency and here in Indiana, the rules for tax sales vary by county.
I guess my thought for trying to buy another investor's lien was that if I offered them more than they would get if the property were redeemed, it would be in their best interest to sell the lien to me. Cash in the hand is more valuable to me than having it tied up in the hopes that the property is redeemed in the next 6 months. My views obviously don't reflect every other investor's views though.
In my opinion, this particular property is highly unlikely to be redeemed. I've already tried to contact the property owner, and I never received any response. A couple of other locals have told me that they've tried to purchase it too and never received a response either. Rumor has it that the woman that owns the property gifted it to her niece, but nothing in public records indicated that that ever happened.
Anyway, I think this has been a good thought exercise. It's good to hear that at least I'm not the only person to have ever thought about trying this. It sounds like it's unlikely to be fruitful, but a good exercise for me no less.
Thanks for the help!