What I do stock brokers do with the remaining quantities of stock or shares after trading session is completed?
You mean all the orders which are pending at close of market?
All the pending orders are cancelled at the EOD by exchange, and shares stay in Demat accounts of clients.
Is there any other cases or types
Other cases and types, as in?
As I explained above, these are all pending orders, exchange will cancel these orders by next trading day.