From what I've been told (having never experienced it myself) is that the $1 transaction fee indicates the property was either gifted or inherited.
Typically, if the transfer date is a date after the passing of the owner, then most likely it was inherited from that prior owner after they passed. (with a $1 transaction fee)
If the transfer date is a date before the passing of the owner, then most likely it was gifted from that prior owner, before they passed. (with a $1 transaction fee)
So your cost basis could be the original $1000 paid for it. Otherwise, if you can determine that somewhere in the custody/ownership chain the new owner inherited it after the prior owner passed, then the cost basis used would be the FMV of the property on the day the prior owner passed away.
Assuming the original purchase price of $1000 is the cost basis to be used, with your wife a 50% owner her share of the cost basis would be $500. Having sold it for $16,000 the gain would be $15,500. From that gain she can subtract her share of the selling expenses and she pays tax on the remainder.
Property taxes paid on the property during her period of ownership are not deductible from the gain. That's because those property taxes were deductible as a SCH A itemized deduction for each year she paid her share of those taxes, during the time she owned the property. If she didn't take that deduction each year, or if her itemized deductions never exceeded the standard deduction, that doesn't change this.
