Is it possible for a trigger to update a row in a table using a value that was deleted?
If I understand your question right, what you want is an after delete trigger:

DELIMITER $$
CREATE TRIGGER ad_foo AFTER DELETE on foo
FOR EACH ROW
BEGIN
  update table1 SET table1.state=1 WHERE id=OLD.id;
END$$
DELIMITER ;


Example with just the insert: http://sqlfiddle.com/#!2/974b4/1

Example with insert and delete: http://sqlfiddle.com/#!2/0bf72/1