MySQL: Constraining a set of columns so at least one is not NULL

I am not aware of a way to enforce such a constraint.

As a workaround, you may consider to have two different columns: If you have one column for the data - containing the phonebook id or the string literal, and another column for the data type - either 'exact' or 'wildcard' -, you can set a NOT NULL constraint to both columns. One obvious drawback is that you cannot have a FK constraint to the phonebooks table any more.

You can make triggers to run on before the insert, to check the values and determine if the insert or update should happen or not. A good example for how to create triggers like this can be found here: https://dba.stackexchange.com/questions/43284/two-nullable-columns-one-required-to-have-value