The details about what happens after POW have not been in any way fixed. Usually there is no difference between POW and POS as you can argue that both systems have a barrier of entry which gives a coin value and helps in price discovery.
What exactly do you mean by "Only the rich people benefit of it."? Maybe we can clear up any doubts or misconceptions?
PoS is about betting, that you have the none manipulated file. I'm not deep into cryptocurrencys, but thats what i understood of it. So if poor people betting with their stake-wallet that they have a none manipulated file they have not much to loose. thats why on PoS only rich guys can take part of it. They have to bet that they have the not manipulated transaction file.
Sure both have a barrier of entry but PoW (especially the GPU one) is easy to enter for everyone. But for PoS you need to ensure with your wallet, that you have the non manipulated file.
I'm not 100% sure if i am right but thats what i understood of PoS. If for example only guys with 1 Shift in Wallet would ensure, they would have a too less risk. so they could manipulate the system with 1 Shift.