Where I'm at if I'd just bought it then no. If I got it by earning it and trading if it's above the limits they give then I'm still liable for the tax on those earnings even if I have no way of paying it.
Are you sure you guys don't have a "casualty" tax deduction? In the states, you can file
Form 4684 (Casualties and Thefts) to account for losses from any kind of act of God, hack, theft, etc. where you lost bitcoins. There are some limitations, though.
This is the breakdown for a "tragic boating accident" sort of tax deduction in the US:
(a) The first $100 of loss is not deductible and
(b) The remaining loss is only deductible to the extent it exceeds 10% of the person’s adjusted gross income.
For someone with a $25,000 gross income, and a $5,000 Unrelated Theft loss, they would be able to deduct $2,400 ($5,000 loss, less $100 = $4,900; and 10% of $25,000 Gross Income is $2,500, meaning $4,900-$2,500 = $2,400 allowable loss)."
So, no matter how you came to own the property (investment vs. earned income), you can recoup a big chunk of the theft/casualty loss in tax deductions. Exactly how much you can deduct is determined by your total income.