how to avoid #1265 error changing a value in a table structure

That is avoiding “data truncated” error. You must avoid to replace a value in use.
The right way, if a given value is already applied to some items, is

1. to add the new value (supposed similar to the old) to the table structure
2. search for all the items with old value
3. replace in each item the old value with the new one
4. delete the old value in the table structure