Maybe might make a news story about transaction volume going up and the price might rise a little but that's about it.
Normally I suppose that would be the case. But imagine the extreme hypothetical case where transactions drop to zero (say, because all bitcoin owners decide to hold their coins, or all transactions happen in internal ledgers of "bitcoin banks" without actual blockchain transactions). Would the miners "starve"? Or would they keep mining empty blocks?
As long as the block subsidy still exists, they will simply mine empty blocks and receive the block subsidy as a reward.
Eventually, bitcoin will need a continuous flow of fee paying transactions to provide the necessary incentive for miners to participate. The block subsidy will fall to extremely small amounts, eventually falling to 0 BTC. If bitcoin doesn't ever reach a high enough level of acceptance and use to provide such a continuous flow of transactions, then miners will begin to shut off their equipment and the security of the network will falter.
It would not be productive for a miner to create transactions. At best, they'd be paying themselves with their own bitcoins. That certainly doesn't provide an incentive as they could increase their profits if they just keep the bitcoins and avoid spending resources on mining. At worst, they would create transactions that would be confirmed by some other miner, essentially providing an incentive to other miners to try to destroy their profitability.
