Bill (George Burns) is an elderly ex-vaudevillian performer who lives alone in a large, comfortable home. He awakens to a special alarm clock that activates his home stereo system, waking him to his favorite music. Along the way, Bill looks at photographs of his deceased wife, who apparently used to be part of his act. After breakfast, Bill goes to the supermarket, driving his unique classic automobile, a meticulously preserved 1930s model Pierce-Arrow; he compulsively takes two orange parking cones out of the trunk and places them in the two parking spaces next to his, to block anybody from parking near his car. Inside the market, Bill interacts in a friendly way with two employees, charming them with a magic trick.Kate (Brooke Shields) is a young teenage girl who is in a domestic squabble with an intimidating man named Demesta (William Russ). Kate, who is apparently nude and is wrapped in a towel, has locked herself in a bathroom to hide from Demesta, who pounds angrily on the door and demands to know the details of a drug deal that Kate has fouled up. He screams at her to give him either his money or his drugs. Frightened, Kate escapes through the bathroom window, still wrapped only in a towel, while a policeman suddenly knocks on the front door of the apartment and grapples with Demesta. The policeman chases Demesta down the street while Kate goes in a different direction, slipping down over a hillside staircase and losing her towel in the process. She runs away totally nude.Bill comes out of the grocery store talking to the bag boy about magic tricks, but when he opens his trunk to replace his orange parking cones, they both see Kate lying naked in his trunk, covered only in a deflated tire tube. Stunned and suddenly in a very compromising position (with a naked teenage girl in his trunk), Bill convinces the bag boy that it was just an illusion and he drives away. He stops on a secluded side street to question Kate, who asks Bill to take her to his house. He reluctantly agrees.Bill tries to get Kate to tell him what's going on, but she avoids all his questions, telling him crazy things like that her parents died on the Titanic and that she has no last name. Bill responds sarcastically to her jibes, but he also does his best to help Kate with whatever trouble she may be in. Instead of going to the police, he allows her to take shelter in his home, allowing her to choose some of his clothes to wear and even altering them so they fit her better. Kate refuses to answer any of his questions, and she attempts to escape Bill's house by dropping out of an upstairs window, spraining her ankle in the process. This attracts the attention of Bill's neighbors, Stan (John Schuck) and Sue (Andrea Howard), a nosy couple who try and figure out who the strange girl is at Bill's house.Bill goes to visit his friend Max (Burl Ives), who is a resident of a nursing home. Max apparently lived with Bill before being confined to the facility due to his despondent condition; Max has retreated into his mind and hasn't spoken a word in years, refusing to react to external stimulus. Bill still makes a habit of visiting him daily, cheerfully telling him about everything that's going on. He tells Max about Kate, saying that he feels as if he has to help her, although he doesn't know how. Later, Bill also receives a visit from his daughter, Shirl (Lorraine Gary) and her husband, Harris (Nicolas Coster). Shirl feels Bill is becoming senile and she tries to get him to sign a document that will give Shirl control over his bank account; when Bill refuses, Shirl becomes furious, complaining that Bill is giving away all of his money, but Bill angrily rebuffs her.Meanwhile, Demesta is in a rage about Kate's betrayal. He questions Roy (Christopher Knight), a teenage friend of Kate's, in an intimidating way and tells him that he'll find Kate wherever she is. When Bill goes to get a prescription for painkillers refilled, Demesta sees him in the pharmacy, but is unaware that he is connected to Kate.Stan and Sue step up their interfering and call Shirl to tell her they saw a young girl in Bill's house. When Shirl returns, she demands to see Kate but Bill refuses to let her in the house. He also refuses to acknowledge that he's harboring a juvenile, denying anything is wrong, much to Shirl's dismay and fury. Shirl suggests to Harris in a private moment that her father has been unstable ever since his vaudeville career went bad, identifying a disatrous show in Pittsburgh as the turning point. Harris thinks Shirl just misunderstands Bill, and encourages her to accept Bill's eccentric ways.Bill and Kate have a conversation where she reveals to him that she's on the run from a drug dealer. She claims Demesta gave her money to make a connection and pay for a cache of product, which she then threw into a sewer in a moment of panic. Bill tells her to go to the police, but Kate is afraid to do this because of the consequences for herself. Bill is happy that Kate has opened up to him finally; he genuinely likes her and feels that she has never had a nurturing home, being shuttled between foster homes. He invites her to come live with him, but Kate tells him that one has to be a certain age to be a foster parent. "I'm not old enough?" he jokes.Bill's poker buddies, whom he calls the "No Shirt Gang", all arrive to play cards at Bill's house, and he introduces Kate to them. They promise to be discreet about her presence, and the evening is interrupted when Shirl makes good on her promise to return with the police. The No Shirt gang hides Kate with a magic trick, levitating her up to the ceiling. When the girl can't be found, Shirl is even more furious.The next day, Bill leaves for his daily visit to Max, and he has a conversation with Kate, explaining Max's situation to her. Kate feels as if Max may need some tough love, recalling a young boy she once knew who also refused to talk. Kate tells Bill that the boy started talking once all the other kids ignored him. When Bill visits Max, he tells Max that he will never come to see him again; unless Max talks, it's goodbye forever. As a result, Max breaks down and begs Bill not to leave, and they embrace. Bill returns to the house excitedly to tell Kate the good news, but he finds that Kate is gone and the house is empty. Bill is despondent.Meanwhile, Kate returns to her foster home and gets a few of her belongings. She meets up with Roy at school, and Roy warns her that Demesta is looking for her. Then Kate reveals what really has her scared: she never made the connection in the first place, and still has the $20,000 cash that Demesta gave her to pay for the drugs. Roy is shocked and tells Kate that Demesta will kill her if he finds her, but Kate plans to leave town with the money. When Roy tells Kate that Demesta has been questioning everybody about Bill, Kate is horrified that Demesta knows where she was hiding, and that any moment now he will track down Bill's house and confront him.She returns to Bill's house, unable to leave town without making sure her new friend is aware of the danger he's in. While she is there, Demesta forces his way into the house; Kate has the $20,000 in her teddy bear, but she and Bill manage to subdue Demesta. After a chase through Bill's house, Bill holds Demesta at bay with a sword, forcing him into a large bag covered in padlocks. When they have him incapacitated, Bill reveals that the sword is a fake, one of Max's props from his magic act.With the police summoned and Demesta arrested, Bill and Kate celebrate by drinking tomato juice. Shirl arrives and is terrified when she sees the police at Bill's house, but Bill talks to her about the strange events that have been going on. Then he asks Shirl a favor.We then see Bill back at the rest home; Max is packing his belongings, preparing to go back home with Bill. Bill explains that Shirl and Harris have agreed to act as foster parents for Kate, and that Kate will stay with Bill and Max on the weekends. The film ends as Bill and Max walk out to greet Kate, who is guarding Bill's car by making sure nobody parks near it.