Certified GKH Gardening Expert
This sounds like how the plant grows naturally. You can prune out anything dead and make an attempt to divide the plant into multiple containers. It won't hurt to leave them, though. The stems should die back once you remove the tubers for winter or put the containers into dormancy.
This article will give you more information on the care of cyclamen: https://www.gardeningknowhow.com/houseplants/cyclamen/cyclamen-care.htm