If the attachment of one brake block failed, I'd be very suspicious of the rest of them. It might be a good idea to replace ALL the rivets with screws, one at a time so you don't lose the alignment of the brake blocks with the shoes. Brass screws won't score the drums, if the linings wear down that far.
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. - Ernest Hemingway
Love your enemies and drive 'em nuts!