If a column has several rows, i.g.:
'red' 'NULL' 'red, yellow' 'green' 'NULL' 'yellow, green'
And you want to add a new string (‘blue’) to every row, so that the result be:
'red, blue' 'blue' 'red, yellow, blue' 'green, blue' 'blue' 'yellow, green, blue'
you can use this code
UPDATE my_table SET mycolumn = CONCAT('same new string ',mycolumn);
But the above code works only for rows with some content, not for the empty (NULL) ones. Therefore you can complete your task with the following:
UPDATE my_table SET mycolumn = 'same new string' WHERE mycolumn IS NULL;