The shift cuts rep­re­sent a sudden, harmful side effect for workers, who at ral­lies and through social media have urged loyal cus­tomers to boy­cott Market Basket stores in hopes that falling rev­enues would compel the company’s board of direc­tors to rein­state their former president.

Instead the board — con­trolled by Arthur S. Demoulas, Arthur T.’s cousin and rival — rejected Arthur T.’s offer Sunday to resume lead­er­ship of Market Basket while terms of a pos­sible sale are negotiated.

The ability of Market Basket’s board to hold to its posi­tion, while workers bend to eco­nomic real­i­ties, reveals an imbal­ance of power in the public struggle for con­trol of the com­pany, said Ted Clark, director of the Center for Family Busi­ness at North­eastern University.

If you’re an hourly employee and you lose a pay­check, that hurts,” Clark said. “But a guy with as much money as Arthur S. can hold out for a long time.”

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