With the sharp stock-market decline for Citigroup rapidly becoming a full-blown crisis of confidence, the company’s executives on Friday entered into talks with federal officials about how to stabilize the struggling financial giant. In a series of tense meetings and telephone calls, the executives and officials weighed several options, including whether to replace Citigroup’s leadership or sell all or part of the company. Other options discussed included a public endorsement from the government or a new financial lifeline, people involved in the talks said. The course of action, however, remained uncertain on Friday night, these people said, and other options...