I don’t know which state you belong to, or are speaking of, but as far as I know, mop up rounds do allow fresh registrations.
The vacant seats irritate the people conducting the counselling & they want to get rid of them as soon as possible. So, they invite all people interested to join the counselling.
After mop up, sometimes, walk-in counselling is conducted – yes, again to get rid of the remaining seats left after mop up. And in walk in counsellings, anyone qualifying NEET can come – they don’t even need to register again.
I’m not sure if this applies for all states or if this will happen this year. But, this is the way it happens all the time.