The Halachic authorities addressed the case of a person reciting Birkat Ha’mazon over a cup of wine, and has only a "Kos Pagum" – "defective cup," meaning, a cup from which somebody had drunk. A "Kos Pagum" should not be used for a Beracha, but it can be "fixed" by adding some wine or water to the cup. The question arises, however, as to what one should do if he has no wine or water available to add to the cup. Should he use this cup, since although a "Kos Pagum" is not optimal, it may nevertheless be used? Or, it is preferable in this situation to use a different beverage, such as beer?
Different views exist among the Poskim, but the final Halacha is that one should use the "Kos Pagum" in such a case. Rav Haim Vital (1543-1620) maintained that Birkat Ha’mazon should be recited only over wine, and not over other beverages, and so it is preferable to use a cup of wine that is "Pagum" than to use a cup filled with a different beverage.
Summary: If the only cup of wine available for reciting Birkat Ha’mazon is "Pagum" – meaning, somebody had drunk from it – and one has no wine or water to add to it, he should nevertheless use that cup, even if he has another beverage – such as beer – available.
