What does it mean when someone is officially closed?
Hi
It means that the record on the 1939 Register is redacted (with a black strip). This applies to anybody born less than 100 years ago whose death has not been confirmed.
We can look for another one of yours by popping in a date of birth!
So trying 5.12.1902 to look for John, and the free index has 20 Browns born on that day.
One is
John C Brown, born 1902, living at 2 Windsor Terrace, Failsworth, Salford C.B.
Could C be a misreading of E?

It also says that George H Brown and 4 more people are on the record, plus 2 more people who are officially closed.
More details are
George H Brown born 1895
Eliza Collinson (Brown)1898
Arthur Brown 1924
Eliza will be Eliza Brown, her surname having later been altered to Collinson.
So George and John should be your Brown brothers, still living in Salford, just like their sister Annie.
I too think it quite possible that Annie the mother reverted to the Brown name and, if so, that probably won't help in finding her death!
Unless she hitched up with somebody else of course!
John