A manicurist, Miss Weldon, arrives in a small town and her bus stops to avoid running over a man. The man, Odd, lies down in the street next to the curb, closes his eyes, and pretends to be dead. The sheriff tells him to move while Miss Weldon goes to the barbershop where she has a job ready. The owner, Mr. Simpson, tells her that she can get a room at a nearby boarding house. Once Miss Weldon leaves, Simpson explains to his customer, Gilpatrick, that Miss Weldon is an old maid and lived with her mother until the older woman died.
As Miss Weldon settles into her job, she watches as Odd continues to lie in the street every day, feigning death, and the sheriff moves him along. Simpson figures that he does it for the publicity. Miss Weldon goes on with her life, eating alone, living alone in her rented room. One night she sees Odd walking on the street past her window.
Odd eventually gets a job cleaning up at the grocery store. One day he leaves with a kitten. Miss Weldon is walking by and notices, and asks to see it. When he shows it to her, and admits he was going to drown it, she asks to keep it, saying drowning is a terrible way to die. Odd agrees, saying that he has drowned.
While she works at the barbershop, Miss Weldon hears Simpson's explanation about Odd's strange behavior. He tells her that a flood washed away Odd's former 20 years ago. Odd disappeared for a few weeks, and then mysteriously appeared. He said he had died and was now a walking dead man.
As Odd continues his daily ritual of playing dead, Miss Weldon offers him some cologne to keep cool. Simpson and Gilpatrick watch, and discuss Odd's life as Miss Simpson returns to work. When Gilpatrick makes a joke about Odd getting married, Miss Weldon "accidentally" cuts his nail too short, hurting him. As they talk about Odd, one farmer suggests that they joke about Odd because no one is quite sure if Odd is dead, and even the doctor has avoided confirming if the man is alive or dead.
Miss Weldon pays regular visits to the grocery store where Odd works. One day a young boy, Charlie, approaches him and says that he knows Odd is dead. Charlie admits that he tried to be dead once, but he couldn't keep pretending. Odd admits that he considered going to a doctor to have himself declared dead, but never got around to it. He explains to Charlie that sometimes he feels alive when Miss Weldon is near. As Charlie leaves, Miss Weldon comes out of the store and asks Odd to walk her home. As they walk, Miss Weldon notices a beautiful dress in a storefront. Odd finally gives his given first name, John and admits that he has $5,000 saved away. He wonders why she likes him, and Miss Weldon says that he's the only man in town who has treated her with respect. She suggests that he stop saying he's dead, and believes he only thinks that way because he doesn't have a woman in his life. Odd isn't convinced.
On Halloween, Odd buys the dress for Miss Weldon. Four teenagers approach him and ask if he'll come to their Halloween party so he can scare them. He notes that he doesn't have a costume, but they say he's scary as is. He refuses and they run off. Odd then goes to see Miss Weldon and sows her the dress. He wonders if he scares her and Miss Weldon says that he doesn't. Odd asks her to marry him and says that he loves her.
Odd gets a haircut at the barbershop and Simpson and the others soon realize he's getting married. He tells them that he bought a small place outside of town, but none of them know what house is available. As he leaves, a real estate agent comments that knows every house in town that's available, and Odd hasn't bought any of them. As the men come out of the barbershop, they see Reverend Polk and ask him about the wedding. Polk has no idea what they're talking about.
That night, Charlie overhears his parents talking about Odd's wedding. He sneaks out and sees Odd and Miss Weldon walking down the street, Miss Weldon in her new dress. He follows them to… a cemetery. Odd leads Miss Weldon into a mausoleum. Charlie steps out and says that it isn't legal for them yet, and says that they are now man and wife. They smile their appreciation, enter the mausoleum, and close the door quietly behind them.