One of the attacks on PBFT protocol is to split network in half, send block to one half, do not send anything to other half and the proposer wents offline and r

One of the attacks on PBFT protocol is to split network in half, send block to one half, do not send anything to other half and the proposer wents offline and restore connectivity between the rest of the nodes. In that case, without any stakes, half of nodes will be locked to NIL, half - to a valid block. In case of stakes, byzantine proposer (it is only one node that is really byzantine, but it can control how network is split) can partition network according to a proportion of stakes, so that neither half gets prevalence. The algorithm in the link you provided does nothing in that case. The only node that will be punished is a byzantine validator which does not care. The system will be in no-progress-possible state indefinitely.