The first sign that something was amiss at UnitedHealth Group’s investor day was when Brian Thompson didn’t show up to his early morning hair and makeup appointment.

At around 6:40 a.m. on Wednesday of last week, Thompson, 50, was shot outside the New York Hilton Midtown hotel in a killing that gripped the world. On Monday, police arrested a man in connection with the shooting who local officials found in Altoona, Pennsylvania, carrying a gun and a handwritten three-page manifesto decrying the health care industry’s profit motives. While the police investigation unfolds, the $500 billion health-care company is simultaneously trying to cope with the personal tragedy of losing a top executive and a spiraling PR crisis that risks long-term reputational harm in a country where so many have turned against it.

Interviews with people familiar with the events show a company under siege.