The kingdom of Saudi Arabia donated more than $10 million. Through a foundation, so did the son-in-law of a former Ukrainian president whose government was widely criticized for corruption and the murder of journalists. A Lebanese-Nigerian developer with vast business interests contributed as much as $5 million.

For years the Bill, Hillary and Chelsea Clinton Foundation thrived largely on the generosity of foreign donors and individuals who gave hundreds of millions of dollars to the global charity. But now, as Mrs. Clinton seeks the White House, the funding of the sprawling philanthropy has become an Achilles’ heel for her campaign and, if she is victorious, potentially her administration as well.

With Mrs. Clinton facing accusations of favoritism toward Clinton Foundation donors during her time as secretary of state, former President Bill Clinton told foundation employees on Thursday that the organization would no longer accept foreign or corporate donations should Mrs. Clinton win in November.

But while the move could avoid the awkwardness of Mr. Clinton jetting around the world asking for money while his wife is president, it did not resolve a more pressing question: how her administration would handle longtime donors seeking help from the United States, or whose interests might conflict with the country’s own.