First, you can't deduct a loss on personal property. Can you prove (if audited) that you were holding this purely as an investment? (There may not be one single fact that proves it one way or another, but if you sold the car pretty soon after the death of the prior owner, that would support that you were treating it as an investment even if the prior owner was treating it as personal property. The longer you owned and drove it, the less likely you could prove you were considering it an investment.)
Then second, can you prove the fair market value on the date of death? An appraisal is usually considered reliable if it is in writing and signed, and if the appraiser is qualified to appraise that type of item. (The definition of proper qualifications may vary from field to field.). Also, was this an eyeball appraisal or did the appraiser do the proper research into recent sales of comparable items and so on. What the appraiser actually say, and what are they willing to put into writing? Will they say it was informal based on their general knowledge, or will they say they carefully reviewed the condition of the car and recent comparable sales?
It would not be unusual for values to drop in the current economic conditions, the appraised value might have been reasonable 2 years ago and the current price reasonable today, you have to prove it.
Just remember that you can put anything on your tax return that you believe, but if audited, you have to convince the auditor. The law says the entire sales price is assumed to be taxable income unless you can prove your basis--you have to prove you are right, the IRS does not have to prove you are wrong. I don't think you have to report zero basis even if the appraisal is not adequate to support $20K, because clearly the car had some value. But that's just my informal opinion.
