You are still talking about absolute poverty, not relative poverty. If somebody got seriously ill and could no longer afford food, for example, then that's not just relative poverty, they actually have a serious problem.
As for "running as fast as you can just to stay in the same place", well that depends. Why would I need to advance? I already have everything I need. I don't work at all, and disasters aren't likely to be much of a problem since I don't have a lot of expensive assets to lose. If I ever need healthcare I can use a government scheme (I don't live in the USA btw). So in this regard, you could say my lifestyle is partly subsidised by the government.
As for "running as fast as you can just to stay in the same place", well that depends. Why would I need to advance? I already have everything I need. I don't work at all, and disasters aren't likely to be much of a problem since I don't have a lot of expensive assets to lose. If I ever need healthcare I can use a government scheme (I don't live in the USA btw). So in this regard, you could say my lifestyle is partly subsidised by the government.