Can I delete a row that is the subject of a query that is deleting it??
If not, how can I do this? It doesn't seem to work and I am wondering
if it is intrinsically impossible or whether there is some other problem.

For example:

BEGIN
FOR SELECT docline.docline_id
FROM docline
INTO :v_docline_id
/* where etc */

DO BEGIN
DELETE from docline
WHERE
docline.docline_id = :v_docline_id;
END
END

Thanks, Mitch