This is a logical error on your part and/or misunderstanding of the term. “Living Wage” is a suggested approximate threshold recommendation based on an average

This is a logical error on your part and/or misunderstanding of the term. “Living Wage” is a suggested approximate threshold recommendation based on an average approximate estimate of living expenses in the region. It is not some value calculated to be that which 100% of living people are achieving. It is not defined as the line above which you’re guaranteed that your life is livable, and it is not defined to mean that if you make less your life is not livable. It is an average, and the line is intentionally drawn to be conservative in the sense that it should work for someone without extra support or being required to cohabitate. Obviously different people have different levels of support, different living standards, different amounts of sharing. It can and does actually occur all over the world that people make less than a living wage, and still manage to live. They’re very poor, and most are unable to escape being poor, but living. They are below a living wage, but that doesn’t make them the contradiction, it is the reality of poverty - the reality is that many people really are living on means below what economists consider a minimum acceptable level.