How Does a Hybrid PoW/PoS System Determine the Block Proposer?

In a hybrid PoW/PoS system, the PoW mechanism is typically used to determine the initial block proposer (the miner who finds the valid hash). However, the PoS component is then used by the validators to vote on and finalize that block.

For instance, in Ethereum's past hybrid model, a PoW miner proposed the block, but a committee of PoS validators used Casper FFG to provide a fast finality guarantee for that block.