Are you being deliberately misunderstanding now.
Let's try one more time.
You cannot sign anyone (ANYONE) after the squad list has been submitted, empty space or not. That was on the 10th September for the summer window.
We do not know when the next squad (final) squad list has to be submitted. We cannot sign ANYONE after that*
*except in extenuating circumstances as previous caveated.
I'm not "deliberately misunderstanding" anyone.
On reflection, I think we're talking about three related, but essentially separate things.
1. The transfer window. As the term indicates, this is the period during which contract transfers between clubs must be transacted;
2. Submission of squad lists. Again self-explanatory - the PL needs to know that clubs don't have too many players, or ones in the wrong category etc. And since contract details sometimes need to be finalised even after the window is closed (eg work permits coming through late), the list cannot be submitted immediately on 01 September (or 01 February), so a week or two is allowed;
3. The signing of a Free Agent. I think this may be done even after the above two, so long as there is still a suitable, unallocated place available. At which point the PL will update their records accordingly.
In positing the above, I'm not claiming it's correct (it may not be), but neither is it irrational. Nor am I suggesting it in order to have a pop at anyone, or score points.