Can cryptocurrency be insured?

Yes, cryptocurrency can be insured, but generally (and currently) this is only available for institutional investors and currency exchanges, not for individuals. There are a few insurers such as Mitsui Sumitomo Insurance, Chubb, XL Catlin, and even Lloyds of London that offer insurance against cryptocurrency exchange losses such as theft. The cryptocurrency insurance market is potentially a big opportunity for insurance companies in the future as the market matures. Insurance will be one more piece of the puzzle that will drive further adoption of cryptocurrencies. See Bloomberg report on cryptocurrency insurance.