You describe what someone tells you about their own or someone else's difficulties as a sob story when you think that they have told you about it in order to get your sympathy.
Any sob story moved Jarvis to generosity.
sob story in British English
noun
a tale of personal distress intended to arouse sympathy, esp one offered as an excuse or apology
sob story in American English
US
Informal
a very sad story, esp. an account of personal troubles that is meant to arouse sympathy