Will,
There are several situations when real estate has 0 value to someone who owns or could own it.
We deal with a larger bank that offered us several multi family properties because they had such bad problems that it was not worth taking them back and owning them. When people like me pass the banks let them go back to the city for taxes. This is quite common. The bank will always to a BPO and a Phase I and with that info they will decide what they want to do.
The second is land in the hood where the house has been taken down for code violation or for fire. These lots sell for $1 all of the time for recording reasons. I would pay someone to take it off my hands if I could not give it back for taxes.
There could also be a lien worth more than the property.
The last one I can think of is a situation where the improvements on the property need to be razed and the cost to do it exceeds the cost of the land. This would make the property worth 0 in my book.