Is it the actual stem that the blooms were on? If so, then that's to be expected. If it's dying, use a sterile knife or clipper to cut it down, dab it with a little cinnamon. At it's next bloom season, a new stem will grow and you'll get treated to the show all over again!
Welcome to the Orchid Board. How long has the spike been up and about for? Sometimes, its just time for them to die. However, usually, the stem goes after the flowers have fallen off. Not the other way around. Let us know.
Welcome to the Orchid Board. I am glad you joined.
__________________
"We must not look at goblin men,
We must not buy their fruits:
Who knows upon what soil they fed
Their hungry thirsty roots?"
As you've heard, the stems eventually shrivel and "dry" up. This is pretty natural for a lot of Phals. Sometimes you can keep them going and get more blossoms, but usually those second and third growth blossoms will be dismal compared to the first ones. Lots of us (me for one) prefer to cut off the spike down near the leaves and let the plant grow more leaves and then a new spike. The results are typically better (not always, but typically).
By the way, welcome to the board. This place is growing by leaps and bounds and we enjoy all the new attitudes and opinions on issues, so ask away and feel free to contribute when you can.