stalla starts to explain all option strategies with "this strategy involves buying … options and selling … options… "etc however I think that zero-cost collar strategy also involves purchase of the underlying stock… otherwise there would be an unlimited loss potential when the price of underlying goes up due to the sale of the call (at high $X) AND an unlimited gain (untill the stock price hits $0) due to the purchase of the put option (al low $X) the collar strategy however limits upside and downside gains/losses so all strategies involve options only, but this one also assumes that you own the underlying… am I correct?

Yes. I believe the assumption is you are long the underlying stock.

or to put it in other words — if you have the underlying stock already, how do you “protect” it with a zero cost? Collar is a solution. So yes, the strategy itself does not include buying the underlying. You use the strategy because you already have it. - sticky

yes you have to assume you currently own the stock

Why would you buy a collar if you don’t have an underlying? What would you collar?

A dog or cat??