If you're the "owner" of that subfolder, set the owner as someone else. Then when you delete it it will only be removed from your account; the other people with whom it is shared will still have access to it.

Direct answer

Tell your students to add your folder shared with them to "My Drive" in their own accounts and that after move or add the corresponding files to that folder.

Explanation

Files owned by the user can't be moved to "Shared with me". At the "root level" of "that place" only could be items that are owned by others could be listed.

Users could organize their own files and folders and files and folders shared with them in "My Drive".

References

Organize your files in Google Drive - Google Drive Help