The story is about a man whose face changes to the identity of different people, according to who he is talking to. At the end, he dies and his face shuffles rapidly through all the identities it has had.
What is the name of the story?
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LaFarge and his wife Anna have forged a new life for themselves, but they still miss their dead son Tom. A night thunderstorm startles the elderly pair, who see a figure standing outside their home in the rain. Afraid, Anna goes to bed, while LaFarge believes that somehow Tom is standing before him. He leaves his house unlocked.
When morning comes, "Tom" is busy helping Anna with chores. LaFarge sees that Anna is somehow unaware of Tom's death, and after speaking privately with him, LaFarge learns that "Tom" is a Martian with an empathic shapeshifting ability: the Martian appears as their dead son to them.
Later that day, Anna insists on a visit to the town. "Tom" is deathly afraid of being so close to so many people. LaFarge promises to keep him close, but at the town they become separated. While searching for "Tom", LaFarge hears that the Spaulding family in town has miraculously found their lost daughter Lavinia. Desperate to avoid a second devastating heartbreak to his wife, LaFarge stands outside Spaulding's home and finds "Tom" now masquerading as Lavinia. He is able to coax "Tom" to come back, and they run desperately back for their boat to leave town. However, everyone "Tom" passes sees a person of their own—a lost husband, a son, a criminal. The Martian, exhausted from his constant shape-changing, spasms, and dies.
The Twilight Zone, Season 1, Episode 13, The Four of Us are Dying
Arch Hammer arrives in the city and checks into a seedy hotel. He looks like any other man but looks can be deceiving. Hammer has the ability to change his appearance at whim, a trick he definitely uses to his own advantage. He takes on the appearance of the recently deceased musician Johnny Foster. who died in a car accident. He goes to meet Maggie, a lounge singer who is mourning Foster's death and convinces her to run off with him. He then takes on the appearance of Virge Sterig, a gangster whose bullet-riddled body was recently found in the river. He then visits mob boss Penell who double-crossed him to get his share of the money their most recent job. An unplanned change of face doesn't go over well however.
Based on a short story by George Clayton Johnson (as George Johnson).