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Without reaching supermajority, multiple competing blockchains can cause a loss of confidence, insecure network due to miners splitting to other chains, confirmation issues, and will in general be bad. This is why any code that involves any sort of fork, contentious or not, requires a supermajority before the node begins to enforce the new rules.
Is there any code change in a hard fork that prevents miners from continuing to mine the old chain, like changing the magic bytes, or changing the version number and adding code that blocks nodes running an earlier version number?
Part of the validation is to check the version number. If the version number is not a certain number or higher then the block is considered invalid and it is rejected. Miners will never mine on an invalid block.