If you didn't have a cost in before and then put one in, your gain correctly went down, meaning you don't have to pay as much in tax on that transaction.
For example, if you sold the item for $100:
$100 sales price - cost unknown = $100 gain
$100 sales price - $50 missing value = $50 gain.
That means that you don't pay tax on as much gain. Your scenario is correct.