Just like witnesses can choose not to include transactions in their blocks, they can also choose not to include blocks in their blockchain.
In such a case, witnesses that agree the block shouldn't be included will build the same local chain on their systems. Witnesses that don't agree will build a different chain on their computers that includes it.
At some point, there's code that tells the witness to switch to the longest of the two competing chains (although even that can be changed via software).