The National Restaurant Association gave $35,000 — a year’s salary — in severance pay to a female staff member in the late 1990s after an encounter with Herman Cain, its chief executive at the time, made her uncomfortable working there, three people with direct knowledge of the payment said on Tuesday.

The woman was one of two whose accusations of sexual harassment by Mr. Cain, now a Republican candidate for president, led to paid severance agreements during his 1996-99 tenure as the association’s chief. Disclosure of the cases has rocked Mr. Cain’s campaign just as he was surging in polls.