Yes. A banana plant (tree) dies after it produces fruit, some quicker than others. But have no fear. If it hasn't already, the rhizome of the mother plant should produce pups. That's where you want to focus now.

-Ray

What to do with it now? Do we cut it down? If so how? like to the dirt level or below? It lives in a greenhouse full of orchids.
Thanks

Cut down the stem that produced the bananas. Soil level is fine, no need to go deeper and risk damaging what's below. What ever sticks above will just turn brown and dead. The root structure called the corm will send up new shoots, if it hasn't already.