While moving my orchids outside for the summer, I broke a catt budstalk with multiple buds, the first one just open. I decided to put it in a small vase rather than just pitching it.
Two weeks later the third bud is opening and the first one has finally dropped off. The tiny vase is on my kitchen windowsill and I may have enjoyed the blooms more there than had they been on the plant! There are two more buds yet to open, but I doubt that it will last long enough for the last one to open.
So if you accidentally break off a budstalk, don't just throw it out, enjoy it in a vase.