How to use LIKE with subquery? In a SQLITE3 DB, I have a table A with a column 'word' containing search words that partially match a column in another table B.

I'd like to SELECT all rows FROM table B WHERE B.name LIKE %any_of_the_words_in_a.word%';

My first idea was to use a REGEX, but I can't get it to work with REGEX and a subquery.
I think this is what you are after, no need for Regex. It's just a correlated subquery, with the only difference being the LIKE condition instead of the common equality condition:

SELECT b.* 
FROM tablename AS b 
WHERE EXISTS 
      ( SELECT * 
        FROM words AS w 
        WHERE b.name LIKE '%' || w.word || '%'
      ) ;