Mrs. Clinton has always been circumspect about Mr. Weiner and her feelings toward him. She has steadfastly supported Ms. Abedin, 40, as the younger woman stood by her husband, despite the public ridicule and career damage that resulted from his behavior. The Clintons have never publicly criticized Mr. Weiner.

It was only two months ago that Ms. Abedin announced that she was separating from her husband, after she learned that The New York Post planned to publish a story reporting that Mr. Weiner had sent a picture of his crotch to a woman online as he lay next to the couple’s 4-year-old son in bed. Mrs. Clinton was vacationing in the Hamptons at the time and stayed away from the story.

Privately, aides to Mrs. Clinton suggested on Friday that Ms. Abedin would remain alongside Mrs. Clinton for the final, breakneck stretch of the campaign. But some senior Democrats are now wondering whether, if Mrs. Clinton is elected, she will be able to bring Ms. Abedin along with her for what was once widely expected to be a senior role in the White House.

Mrs. Clinton’s loyalty to Ms. Abedin (and vice versa) stems from the decades they have spent working closely together, beginning when Ms. Abedin was a 19-year-old intern to the first lady in the 1990s.

At the State Department, Ms. Abedin served as deputy chief of staff to Mrs. Clinton. Emails released by the State Department captured the closeness of their relationship. A jet-lagged Mrs. Clinton once emailed Ms. Abedin at 12:21 a.m. to take her up on an offer to come over to Mrs. Clinton’s house for a chat. “Just knock on the door to the bedroom if it’s closed,” she wrote.