Refer to UTXO by output index or output full address in blockchain?
In Bitcoin, it was originally an assumption that miners producing blocks would use a unique address per transaction, making sure that the coinbase of each block had a unique TXID. As this was not enforced, users accidentally made duplicate transactions by setting the same destination address for multiple solved blocks. BIP34 simply adds a new field to be validated to the block, requiring that the height is also part of the hash, ensuring uniqueness for all future blocks.
For the two special cased BIP34 blocks, the outcome is rather simple. The first instance of the TXID creates the UTXO, the second invocation does nothing at all because the output already exists, and if they were ever spent the UTXO can only be removed from the database a single time. The money involved in the second instance of the TXID was destroyed, causing a loss of 100 BTC total.