I did also find this document from the OECD:
For example, in the case of loss or theft of a crypto-asset in Australia, the owner may claim a capital loss, provided they are able to present the evidence of their ownership.
So I am an Australian. I have Bitcoin in a wallet that I can prove belongs to me. For example, I purchased the coins on a centralized exchange where I performed KYC. I withdrew them from there to my wallet and that should be enough to prove they are mine. To avoid paying taxes, I "lose" my coins. I send them out over TOR to another Bitcoin wallet. From their, they get mixed, coin-joined, converted to Monero, gambled with, etc. Omg, I am so unlucky, someone stole my coins, but thankfully, I can claim capital losses.
I wonder what the Australian authorities would say to a claim like that.
US here, but I am going to guess the same thing that happens here when anything is stolen that cannot be traced. The government accepts you at your word. And, if it ever comes out or can be proven that you lied you get arrested and charged with fraud.
It also is probably one of those things you can only do once. If it happens again, although they might let you claim it, they are going to look through all your finances very closely and see if they can find anything that is "not correct".
Kind of like a lot of stolen art fraud. Buy expense art, sell it under the table, claim theft, collect insurance.
-Dave