Technically, nothing. This is essentially what happened when Ethereum Classic was created - some of the miners rejected the hardfork and continued to mine the old chain, which still exists and is now known as ETC.

However, Ethereum has a built in "difficulty bomb", which makes mining new blocks become exponentially harder over time, until eventually mining a new block becomes impossible and chain freezes - known as the Ethereum "ice age". One of the EIPs (EIP 1234: Constantinople Difficulty Bomb Delay and Block Reward Adjustment) in this hardfork will push that back. If miners do not adopt the new chain, they will be stuck mining a chain that is rapidly becoming more difficult, less profitable and eventually obsolete.