Really rich people are not affected as much by inflation as they take out loans to pay for their day-to-day life which is then paid back in the currency that is inflating, while it's paid with the interest they earn with company shares. Those shares are not directly hit by inflation like the loan is.
This lifestyle/procedure makes it easier to maintain your wealth compared to a regular person.
See in your example you say company value rose by 4% and inflation by 8% so they loose money, but that also means the company performed worse than before. Think of it like gold, when I have 1 ounce of gold and the dollar value sinks due to inflation, the value of my gold did not change, it's still one ounce of gold and if the gold price is not sinking for some reason, the cost/buying price of gold will most likely rise 8%, because the currency is worth 8% less but the value of gold staid the same.