Yes, a share or a cryptocurrency can become worthless.
The simplest example is when a company ceases trading. At that point any remaining assets will be sold off and used to pay outstanding debts. Any money left over will be returned to the shareholders as cash. In most cases there won't even be enough money to cover the outstanding debts, so shareholders get nothing.
With a cryptocurrency there isn't even a company with assets to sell. Many people buy cryptocurrency because they think the price is going to go up because of other people buying cryptocurrency. If everyone thinks that a particular currency is overvalued, then the price will reduce and there is nothing to stop it reducing to zero. A price of zero just means that no one wants to buy it from you, however cheaply you offer to sell it to them.
Unless you are very confident you understand the risks and what you can lose, you should always take professional advice before making any investment.