Well, then these nodes will stop if the block chain has a single block on it not signalling segwit.  If you want to use that node, you cannot do any transactions any more.  If you would start such node right now, it would simply stop at the first non-segwit signalling block.  It would find that the next block (segwit signalling) is not one built on the last one that is valid according to him, and will never find any other block any more that suits him.  So he stops.    But the miners don't stop.  They continue to make the chain like they make it today.  

What's the difference between running such a stopped node left behind, and switching off the machine on which it runs ?

People (users) wanting to transact coins, will avoid your full node to connect their SPV wallet to, because your node is not at the current height.   If all non-mining nodes do so, it is as if all of them switched off.  So users will ultimately only connect to miner nodes.  In a certain way, this looks somewhat like a sybil attack on the P2P network, by introducing a lot of nodes that have wrong data (stopped chains).  But as we know, the P2P network doesn't mind Sybil attacks.  Users wanting to transact will quickly blacklist them, to only connect to up-to-date nodes - ultimately, the miner pool data centers.

Suppose that an exchange installs such a node.  Suddenly, its customers cannot withdraw any more or cannot deposit any more.  I'm sure they are going to like it !  They will all run to an exchange that keeps accepting withdrawals and deposits.  They will convert all their holdings on the former exchange to LTC, ripple or ETH, withdraw, and deposit on the exchange that keeps allowing bitcoin transactions on the sole chain that exists.  And never go back to the former exchange again.  (*)

Note that nobody can "vote in the market" as long as there is a single block chain, because you only have wallets that work, and wallets that don't work.  Users, and exchanges, will prefer wallets that work.

(*) come to think of it, an exchange might very well do this temporarily, to make its customers sell their BTC they cannot withdraw for cheap, to switch back to a normal node afterwards, and reap in the difference !