I have a red hibiscus and it also leaves the stem on the plant after the flower drops. You may have noticed that the stem will fall off later. I usually just wait until the stem drops. I think this is normal.

I have taken my annual hibiscus inside the house for the winter. It will drop its leaves and look very dead. But, come spring it will begin to sprout new leaves and when the weather gets warm I will bring it outside once again. Good luck with your hibiscus. I hope you were able to save it before the frost.