Former President Donald J. Trump received a subpoena this spring in search of documents that federal investigators believed he had failed to turn over earlier in the year, when he returned boxes of material he had improperly taken with him upon moving out of the White House, three people familiar with the matter said…

Some senior Republicans have been warned by allies of Mr. Trump not to continue to be aggressive in criticizing the Justice Department and the F.B.I. over the matter because it is possible that more damaging information related to the search will become public.