An obscure options related question?

It is not an obscure question at all. It happens regularly.

When the company is bought out, the option is adjusted and the underlying becomes whatever the owner of 100 shares of the stock received in the buyout.

For example, if the buyout was for $15.10 per share, the underlying become $1,510 per contract. If the buyout was for 5.5 shares of the new company for each share of the acquired company, the underlying become 550 shares of the new company.

Options are also adjust for splits and special dividends. (A dividend is usually considered special if it 10% or more of the stock price.)

You can look up current and old adjustments at

http://www.cboe.com/tradtool/contracts.aspx

to see examples.

It remains yours, the same for stocks, if you don't want to sell, you may keep them, be it voting or non-voting stocks.

How would they take stocks out by force from people? They don't its illegal.

What really happens during takeovers its that they buy the stocks the company and the directors hold.