> Perhaps in the modern era, but less so in the past. The IRS also has a workaround if you can't prove your tax basis, which is to consider it all gains. That's a reasonable fallback for calculating gains, because if you don't have proof of basis, it's likely to be an older acquisition (and one which is more highly appreciated.) But the opposite is true for inflation adjusting, which would leave people with no records to be considered to have zero tax basis (all gains) and no inflation adjustment.

If lacking transfer documents makes the sale value “all gains”, then the inflation adjustment is irrelevant, since you are adjusting a zero basis value, which is still going to be zero if you do or don't adjust it for inflation, no matter what a amount of inflation has occurred.

The only place where there is even a theoretical problem is where there is proof of basis value but not basis date; this seems extremely improbable to occur in practice.