The Slender Thread (1965)

Alan is a Seattle college student volunteering at a crisis center. One night when he's at the clinic alone, he takes a call from a woman who tells him that she needs to talk to someone. She informs Alan that she took a load of pills, and he secretly tries to get help. During this time, he learns more about the woman, her family life, and why she wants to die. Can he save her in time?