Willard R. questions: Is it possible that there is a 1955 doubled die Lincoln cent in the grade of PROOF?
To my knowledge there are no 1955 double die proofs.
Doubled dies are improperly made dies. A new die is struck several times by the master hub; if there is any rotation, parts or all of the design can show misalignment or doubling. Because the dies are struck multiple times to impress the design deeply in the metal, minor doubling is fairly common and virtually unnoticeable except under magnification. Note that every coin struck with a doubled die is identical.
Though many dies are used to strike coins in any given year, only one of the 1955 dies was terribly flawed. It is amazing that no one noticed the obviously doubled obverse image until the coins were already outside the Mint. Note that there are other minor doubled dies from this year.
Since modern proof dies are made differently and the resulting coins are struck one-at-a-time and examined for flaws, it is much less likely that such an obvious defect would go undetected on proofs. By the way, proof is not a grade but a method of manufacture.