in any active network you are going to see lost coins; from people sending to incorrect addresses, to people losing their .dat files, etc, so if you have 0 rewards then it essentially means that the currency would be deflationary, and people have no incentive to stake. So all you have to do is have a staking reward that is just high enough to make up for lost coins, the overall supply won't increase but people will still have incentive to support the network. Monero's (PoW) planned tail-emission I believe is designed for this exact situation, I'm sure you could do something similar with PoS.
But I don't think you get what the original post means. If I understand it correctly, he wants to use the blockchain technology for something else, not used as a coin, but other things like to record transactions. The coin will be most likely used as an invisible token, in which case you would not worry about the lost of coins. Let's say, if I build something to record all transactions of a stock, from the IPO time to the end (maybe delisted or being bought), all transactions can be recorded in the blockchain (which acts like a distributed database - the real difference with a distributed database exist today (such as cassandra) is that it is tamper-proof, of course it is run by a bunch of nodes, say each stock dealer run a node.
I think it is an excellent use-case, and I will be very interested in it if someone has further ideas with it.
Hi dream, thanks for clarifying. Nice to see you again in the forum!