To re-produce:

1. Create Project A with an associated issue security scheme
2. Create an issue with a security level set and a sub-task
3. Create Project B with no associated issue security scheme
4. Move issue (with its sub-task) from Project A into Project B

Results
The issue is created in Project B but with no sub-tasks visible on the View Issue page nor the Issue Navigator even though the sub-tasks where created in the new project. This is due to the security levels being retained from Project A (as discussed at JRA-10546)

Below are the parent issue and 2 sub-tasks created in Project B

mysql> select id, pkey, issuetype, security from jiraissue where project = '10011';
+-------+-------+-----------+----------+
| id    | pkey  | issuetype | security |
+-------+-------+-----------+----------+
| 10065 | BBB-1 | 4         |     NULL |
| 10066 | BBB-2 | 5         |    10001 |
| 10067 | BBB-3 | 5         |    10001 |
+-------+-------+-----------+----------+

where BBB-1 is the parent issue and BBB-2 and BBB-3 are its sub-tasks. If the security fields above are then updated to NULL for BBB-2 and BBB-3 the sub-tasks are then viewable.

Additionally, if the target project also has a security scheme associated to it the user is prompted to pick a security level to apply to the issue being moved in the move wizard and works correctly.