I've been asked this "We want to start a new Subsidiary and add the subsidiary to the customers / vendors and when we look at the reports, mainly accounting, we want to see the 'balance' for the new subsidiary and not the 'balance' of the 'old' subsidiary" My question is, "Is it Possible ?"

Don't think its possible without a proper data migration of the historical trial balances from the old one to the new one. However, it wouldn't prevent you from seeing the old sub data, even if the old subsidiary is made inactive. Probably your way to go would be closing the last period at the old sub and starting transacting at the new one. Of course you'd have to "clean" any pending transaction (A/R, A/R, etc) and create them for the new sub.