That question is trying to confuse the issue by conflating two ideas and misusing the word subsidize. The taxpayer is not subsidizing Walmart. The government would be subsidizing Walmart if it were paying Walmart directly so that Walmart could keep its prices low. Walmart is able to keep its prices low by keeping its costs low. Walmart has no control over whether or not the government gives out welfare or who the government gives it to, or how much.
Why shouldnt a fulltime worker make enough, without welfare, to live?
A full time worker would make enough if he became more productive. The formula for wage rates is w = (d/s), or in other words, average money wage rates equals demand for labor divided by supply for labor. There is no divine right of stagnation. If a worker wants to earn enough then he should improve himself. There is a higher demand for knowledgeable, skilled, and experienced workers, and less of a supply of them, so they will be able to earn a higher wage rate on average.