It seems there are hypothetical scenarios where your taxes could exceed your net worth. If you mine a bitcoin worth $1000, and then it's value falls to $100, you could owe taxes on $1000, and the $900 capital loss would only carry forward to the next year.
This is pretty much what happened to a lot of people in the valley during the dot-com bubble pop - your stock losses could be carried forward until the heat death of the universe, but you paid on 100% of the (illusory) gains.
For most, the issue was exercising their options. This is a tax event -- and the tax is owed on the difference in your strike price and the current price of the stock. If you find yourself in this situation -- immediately sell enough stock to cover the tax.
If you are given stock -- that is the tax event. You need to have enough cash to cover taxes on stock given to you -- if the stock is illiquid, and this is a bonus or something, then you should ask for part of the bonus to be in cash (to cover tax). If the stock is liquid, immediately sell enough to cover tax.
If you are a founder, and your stock just goes up in price, that is not a tax event.
Being given at-the-money options is not a tax event. You only owe stock tax once you exercise.
IANAA (not an accountant)
EDIT: replace "stock" with "tax" in the second to last paragraph