Another option gives workers the freedom to adjust their schedules, no questions asked, because of unpredictable obligations, like a sleepless night with a toddler or a trip to the emergency room with an older parent. “Nobody wants to be the female in the department who says, ‘My kid threw up on me this morning; I can’t come in,’ ” said Annie Dean, who worked as a lawyer before starting Werk with Anna Auerbach, a former consultant.