With his sharp intellect and steely resolve, Ted Cruz has propelled himself through one accomplishment after another: Princeton, Harvard Law, a Supreme Court clerkship, the United States Senate, and now a strong contender for the Republican presidential nomination.

But as his life was taking off, his half sister’s was going in the opposite direction, a snowballing misery of bad choices, bad luck and, most of all, a losing battle with drugs.

Through her Mr. Cruz became acquainted with a world far from the towers of the Ivy League and the corridors of power — so far that several of Ms. Cruz’s friends interviewed recently did not even know Mr. Cruz was running for president.

He fielded phone calls from his half sister when she landed in jail. He kept tabs on her as she bounced from boyfriend to boyfriend, job to job, and in and out of rehab. He took a particular interest in making sure that her son was cared for, including taking out a large credit card advance to send him to a military-themed boarding school. Ms. Cruz, friends said, came to look up to her younger half brother and to rely on his help.

Image Miriam Cruz in an undated driver’s license photo. Credit... via Collingdale Police Department

But Mr. Cruz, accustomed to achieving everything he set his mind to, also learned the limits of what he could accomplish. Despite periods of sobriety, Ms. Cruz continued in her drug abuse and arrests until 2011, when she died of an accidental overdose in a bedroom strewn with prescription pill bottles.