How to force seting incorrect or nonexistent foreign key index in MySQL?

You can't "force" a value that violates a foreign key. That's the whole point of foreign keys.

Do not use a dummy value such as zero to indicate a nonexistent value. There are only two correct ways to deal with an optional association. The first is to use nulls to indicate no association in a given instance.

The second is to rework your schema so as to conform to sixth normal form.

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