In Ethereum's DAO hack, tokens were also stolen, but they got lucky and the money wasn't spendable for a while (because of how the transaction/contract was written), so they were actually able to convince the entire network[1] to agree to reverse that theft as part of the protocol and recover the tokens that way.
[1] Minus a fragment that became EthereumClassic.
This ability is guarded by a private key. If this private key is stolen, someone else ALSO has the ability to spend this bitcoin.
Then, if this attacker transfers this bitcoin to another of his own private keys (he 'spends' it), in the blockchain there will be a record, yes. But who owns this new private key is unknown.
all the ransomware in the news in recent year or two accepted bitcoin payment to decrypt your data.
This is no different than when a bank is robbed and banknotes are stolen. The bank might have written down the numbers of the banknotes and those can be published. But most shops won't check those when somebody buys something.
Well it's quite a bit different because everyone has access to the ledger where you can see what "bills" were stolen and can automatically prevent them from being used.
Bitcoin's blockchain is just a ledger of amounts stored at addresses at points in time.
Say I steal 10 bitcoins from you. I go to someone who cleans bitcoins for a cost of 10%. I send them 10 bitcoins, and they send 1 bitcoin to 9 different wallets (keeping the 10th as payment). That alone would allow you to still track it. But now add in thousands of other people sending them bitcoins on the same day, and some random pauses as to when they send the bitcoins to other wallets, and you are no longer able to tell which bitcoins in are associated with which bitcoins out.
Now, do you just get businesses to stop doing business with anyone (any wallet) that has ever received bit coins from the mixer? And there are many mixers out there.
And this is still simplified. You can be governments are monitoring and running statistical analysis on those mixers to try to find people laundering bitcoins associated with especially bad things. I'd even guess some of the bitcoin laundering operations are ran by governments in an attempt to better track the flow of bitcoins.
The value of a dollar bill is the same whether it was used in a crime. But if it has some ink on it, it might provide evidence that the person holding it robbed a bank. The ink doesn't keep the dollar from being usable.
It has to be this way. Otherwise money simply gets taken out of circulation, and people participating in the economy have to worry about whether money is money.
More: https://www.reddit.com/r/Bitcoin/comments/1qomqt/what_a_land...
And yes, it's not possible to hide stolen Bitcoin. These addresses will be monitored forever. Think about what would happen if you stole some Bitcoin from the mafia and could not cash it. There are some services that can mix Bitcoin to hide their origin.
It would be possible to fork Bitcoin to reject the transactions used in the theft, thereby restoring the funds. This is what Ethereum did for the DAO hack. But so far, the Bitcoin community hasn't shown a willingness to do this.
Input 1,000 different peoples coins, output any one of their coins one at a time. There's no way to know whose coins are coming out the other side.
You can try to conceal your coins by sending to many addresses, using mixer services to switch your coins with someone else and then trade them often to other cryptocurrencies which makes them harder to track. I would personally try to trade them for Monero where you basically can't trace your transactions.
And with no way to reverse it there's no way to pull the balance back.