While Bitcoin is a global network that functions in a pseudonymous way, it would be extremely hard (if not impossible) to track down the physical identity of Bitcoin holders.
Bitcoin’s price frequently fluctuates whenever governments announce that regulations are or will be applied in cryptocurrencies. As 50% of the global Bitcoin mining is generated from China, the recent ban on cryptocurrency exchanges and ICOs within the country caused a significant plummet in the value of Bitcoin.
It is said that, the governments take such measures to diminish the usage of the digital currencies for fraudulent activities, like money laundering or paying for illegal products in the Dark Web (e.g, drugs). The reality is that governments are experiencing significant capital loses; in China’s case, they have seen over one trillion dollars fly outside the country, while a capital control is in effect.
While Bitcoin is a global network that functions in a pseudonymous way, it would be extremely hard (if not impossible) to track down the physical identity of Bitcoin holders. Furthermore, governments do not understand the cryptocurrencies to their full extent. Regulating the Bitcoin and Blockchain seems non-sensible, but regulating transactions with financial institutions or legitimate merchants could be managed. In other words, one could store his assets in the form of Bitcoin, unaffected by regulations, but could have consequences once he would try to convert them to fiat money or pay for the purchase of a product online.
Given the above, governments are targeting to regulate what is easy for them, the exchanges. That, of course, in the case that a “hodler” wants to covert his Bitcoins because, if the cryptocurrency becomes widely accepted as a payment method, chances are small that someone will ever need to do that.
Additionally, similar bans or restrictions (US citizens are not allowed to participate in ICOs that are not compliant with SEC) could be bypassed, by hiding behind a VPN secure connection or by simply relocating to an unregulated country.
In general, the answer would be that, yes, it is possible, even though it would require impractical and probably unrealistic methods to obtain that. Theoretically, “Shutting down Bitcoin” could be done by switching off the Internet. Clearly, even if closing the Internet was achievable (doubtful,) it would also mean that every governmental and financial institution would have negative impacts, along with Bitcoin.
There isn’t any centralized authority that governs Bitcoin’s network. Even if a government tried to locate its originator, they wouldn’t know where to start. Blockchain uses Peer-to-Peer connections, hence an attempt to halt Bitcoin would probably have no success, same as the governments failed to stop the usage of torrents in the ‘00s.
The most realistic way (and Blockchain’s biggest vulnerability) is the 51% attack. As a new block needs the majority’s consensus to be verified, through the Proof-of-Work method, it would be possible to tamper the validity of the generated blocks by using immense computational power to own more than half of the total mining power. This could be a viable way to terminate Bitcoin, by entering empty blocks in the Blockchain; however, this would demand vast amounts of money for the mining power required.