Even after all Coins are mined (which will probably be in 120+ years) there are still miner who validate transactions and create blocks. There is "just" no block reward anymore.
But Miner wil get paid by TX fees only then. Which should be high enough of value in 120 years
You will get money from the transaction fees, I think.
In Proof of Stake you have to "stake" your coins (means lock them down, you cant use them anymore for a specific timeframe) and you get interest on your staked coins (about 3-8%).