Impossible, miner will just mine empty block (block which only contain coinbase transaction). Here are few example (each from different pool),
My assumption is that he is talking about a side chain with no subsidy, therefore there is little incentive to mine empty blocks.
But there's still incentive, which means someone still mine a block. Aside from security incentive, there's incentive to keep the network alive (as in there's change/update by creating new block) by developer and enthusiasm users. I'm sure developer/enthusiasm users don't mind spare 1 core of their CPU cores to perform mining.