Looks like a complex hybrid Phaleanopsis and Cattleya live arrangement. The flower stems should be able to be cut and rebloomed the next season for all of those plants, but if the flowers fall and the stem stays green you can leave it on the plant and it can potentially make more flowers from that same stem. But based on the shape of the flowers those don't look like sequential bloomers so if they were in my collection I'd cut the stem after the flowers fell to let the mother plant save energy for the next bloom cycle.
That's a beautiful arrangement, too.