A decade ago, the world had a brief fascination with José Mujica. He was the folksy president of Uruguay who had shunned his nation’s presidential palace to live in a tiny tin-roof home with his wife and three-legged dog.

In speeches to world leaders, interviews with foreign journalists and documentaries on Netflix, Pepe Mujica, as he is universally known, shared countless tales from a life story fit for film. He had robbed banks as a leftist urban guerrilla; survived 15 years as a prisoner, including by befriending a frog while kept in a hole in the ground; and helped lead the transformation of his small South American nation into one of the world’s healthiest and most socially liberal democracies.

But Mr. Mujica’s legacy will be more than his colorful history and commitment to austerity. He became one of Latin America’s most influential and important figures in large part for his plain-spoken philosophy on the path to a better society and happier life.

Now, as Mr. Mujica puts it, he is fighting death. In April, he announced he would undergo radiation for a tumor in his esophagus. At 89 and already diagnosed with an autoimmune disease, he admitted the path to recovery would be arduous.

Last week, I traveled to the outskirts of Montevideo, Uruguay’s capital, to visit Mr. Mujica at his three-room home, full of books and jars of pickling vegetables, on the small farm where he has grown chrysanthemums for decades. As the sun set on a winter day, he was bundled in a winter jacket and wool hat in front of a wood stove. The treatment had left him weak and hardly eating.

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