Please note: I am asking the question I want answered. I know this question means the database is set up poorly. So I will vote down any answers that suggest changing
Use:
INSERT INTO table (name, col1, col2) SELECT t.name, t.col1, 'a' FROM TABLE t WHERE t.col2 IS NULL
That's assuming neither the name or col1 columns are a primary key or have a unique constraint on either.
name
col1