Not 100% sure what you're asking...
If you're asking if it's possible to have a directory WITHOUT write permissions (by a particular users/groups), but have a subdirectory WITH write permissions .. yes.
Try it
mkdir ~/test-parent
mkdir ~/test-parent/test-child
chmod 555 ~/test-parent
Now see if you can create a file or folder in
~/test-parent and
~/test-parent/test-childOr am I misunderstanding the question ?
You can delete these test folders (and contents) when you're done testing with: