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Let's assume if U.S went to WW3 in far or near future. If it is the case what would happen to the stocks and companies?
Will the stock fall enough to the point stock would just disappear? what about the company that has headquarters at the place during war time?
What do you mean when you ask if a stock would "disappear"?
If a company was destroyed in the course of a war, like if they had one office and it was bombed and there was nothing left, they might well go bankrupt and the value of their stock drop to zero. In that sense a stock could "disappear".
In general I'd expect that stocks in companies that suffer damage to their assets from the destruction of war would go down. Stocks in companies that produce weapons, supplies for the troops, etc, would likely go up. Stocks in companies that produce consumer goods would probably go down because wealth is being diverted to the war effort.
Beyond that, what happens would depend on the details of the war. If, say, a war was fought in a place that is a major producer of copper, world copper supplies would presumably be disrupted. Companies that use copper would have problems and their stocks would go down. Companies outside the war zone that produce copper would see greater demand for their products and their stocks would go up.
Initially, it'd probably lead to a decrease in value of cyclical stocks (cars, consumer goods), and an increase in defensive stocks (cigarette companies, oil). You'd imagine that any war (in the short-term) would also involve the middle east which would lead to lower oil production. This would obviously increase demand for oil relative to output (similar to what we saw post 9/11). So essentially, a war in the short-term would have all of the effects on the stock market that any market shock has. A rise in the value of defensive stocks, and a decrease in the value of cyclical stocks. Long-term however, as the shock is absorbed, it will be impossible to know where the market will go. After 9/11 we had a relative boom starting in 2003, that was independent of the Iraq war.
