The poor have nothing to protect from inflation: they don't have significant savings, they spend their income the day/week/month that they get it. Their wages should go up to match inflation, and if they don't, its not really related to inflation itself but stingy bosses who aren't sharing increased prices (since given inflation, prices are supposed to rise, right?).

The rich are both lending and borrowing money; again, who do you think they are borrowing money from? Who are they buying the assets from? Again, it is not the poor, unless you are suggesting they are accumulating previously non-existing or non-utilized assets?