Mysql cannot import from text file
error 1366 incorrect integer value: '&quot;&quot;' for column 'word_id' at row 3

This error is logical, basically, an empty string is not a number. That's the first problem.

Also I tried using null, quotes, no quotes, all different types of formatting the data that you could imagine

The problem with this is that if your word_id column is not nullable, you can't insert a null value into it. Also, formatting invalid data doesn't make it valid.

error 1452 cannot add or update a child row: a foreign key constraint fails ('words', CONSTRAINT 'fk_words&quot; FOREIGN KEY ('person_id') REFERENCES 'person' ('person_id'))

This error is normal. This is what Foreign Key constraints are for. Basically, what they do is make sure that you can't insert invalid data when referencing some other data
In this case, you reference a word (As far as I can tell), but you don't have words that have the ID value '' (empty string), so it doesn't allow you to insert the row with an incorrect reference.
Now that the errors are explained, there are two solutions:
1: Allow your word_id column to be null in your table schema. (This is possible even with foreign key constraints, however it might violate your database design). This way, you can insert a NULL value into the word_id column instead of an actual word_id.
2: Fix your data. Basically, you've built your database in such a way that you don't allow an empty or null value for the word_id column, which coincidentally means that your CSV data is invalid in the way that it is an empty string.
You need to update the CSV data to have a correct reference to the word_id column for your data to be 'correct' again.
The so-called 'correct' approach according to how you've set up your database is the second one, where you fix the data. However, both solutions will work. Just make sure to document the changes to your database if you chose solution number 1 because the application which uses the data from your database might not be expecting NULL values and might break because of this.