The dummy address must be an invalid address, and the network would verify this as soon as the client connected. For example, If a real NuShares address has to start with an S, then a dummy NuShares address MUST NOT start with an S. If a bad actor tried to use a real NuShares address with a private key, then the network would not let him connect, and it definitely would not let him exchange NuShares for NuBits. When he or she tried to destroy NuShares or NuBits by sending them to a dummy address, the network would verify that the dummy address was an invalid address. If the address were valid, then the network would reject the transaction.
The Bitcoin network works this way right now. Valid Bitcoin addresses start with a 1 or a 3. You could make up a Bitcoin address that started with a 7, but there could be no valid private key associated with it on the Bitcoin network. You could send coins to the invalid address, but you could never spend them because they would have no valid private key. However, if you looked up the invalid Bitcoin address in a block explorer, it would correctly show the unspendable balance at the invalid address.
The client could randomly generate dummy addresses, but these dummy addresses must be invalidated by starting them with characters that are invalid for authentic addresses.