MySQL: UPDATE trigger. Obtain the value of a column used in UPDATE's where clause if it fail to match any row?

This could be make in a RULE in other database systems (PostgreSQL), that does not exists in MySQL. It's a Rule and not a trigger as you should analyse the query and not the result of the query.

No. An update trigger fires once for each row that gets updated, not once for each update command that's executed. There's no way to make the trigger fire if nothing is updated.

You would need to handle this in your application by checking the number of updated rows returned by your query.

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