For US users, the Tax Cuts and Jobs Act passed in 2017. This lengthy tax law no longer allows for deductions of lost or stolen property as of January 1, 2018. If you lost or had cryptocurrency stolen after that date, you can create a send transaction and mark the coin as
lost / stolen. Depending on the circumstances, you may have additional recourse in a small number of situations to use the IRS code to claim losses on your cryptocurrency. For transactions before January 1, 2018, you can work with your accountant to fill out a Form 4684 for Casualties and Thefts.
If you had a coin becomes worthless (not lose 90% of its value — literally become worthless), you can sell / send the asset to a third party address. This will trigger a full capital loss for the asset. If the coin is coming from a synced wallet or exchange, then this will be automatically registered.
If the coin is completely illiquid and you have no way of disposing it, you can try to take the position that it should still be considered for a worthless asset deduction. This is a grey area of the tax code so continue at your own risk. In this case, you can manually create a send transaction and then edit the proceeds from the transactions page to be USD 0.00000001. This will effectively register as a 100% capital loss on that coin. If you decide to take this position, make sure to keep records showing that you tried all reasonable methods to dispose of the asset first, but it was not possible.
Disclaimer: this post is informational only and is not intended as tax advice. For tax advice, please consult a tax professional.