It depends of course on what the mining node tries to do.
If it stops mining, that is fine, so long as there are sufficient other mining nodes to maintain the configured level of mining diversity.
If it broadcasts an illegal block, this block will not be accepted by other nodes in the network.
If it broadcasts too many illegal blocks, it will be throttled by other nodes in the network and eventually it will no longer be listened to.
To detect the problem: On any node you can monitor the banscore fields in the output from getpeerinfo to spot nodes which are sending illegal blocks (or doing other illegal things). You can also use listblocks to review the miners of the last X blocks, to see if one of the mining nodes has stopped participating.
