INSERT INTO parent_of (id, parent_id, isdir, name)
VALUES (1, NULL, 1, 'root')
     , (2, 1, 0, 'file1')
     , (3, 1, 1, 'dir1')
     , (4, 1, 0, 'file2')
     , (5, 1, 1, 'dir2')
     , (6, 5, 0, 'file3')
     , (8, 7, 0, 'file4'); -- last one is orphan
/* paths:
1   root
2   root\file1
3   root\dir1
4   root\file2
5   root\dir2
6   root\dir2\file3
*/

INSERT INTO parent_of VALUES (7, 5, 1, 'dir3'); -- orphan is resolved after this is inserted
/* paths:
1   root
2   root\file1
3   root\dir1
4   root\file2
5   root\dir2
6   root\dir2\file3
7   root\dir2\dir3
8   root\dir2\dir3\file4
*/

UPDATE parent_of  -- move entire subtree '/dir2' to '/dir1/dir2'
SET parent_id = 3
WHERE id = 5;
/* paths:
1   root
2   root\file1
3   root\dir1
4   root\file2
5   root\dir1\dir2
6   root\dir1\dir2\file3
7   root\dir1\dir2\dir3
8   root\dir1\dir2\dir3\file4
*/