It may be Austrocylindropuntia subulata - here is a close-up of that plant:

One of the stems/trunks looks damaged at the soil line, perhaps rotting. This happens when plant is over-watered. Are they all soft? The plant should be erect.

Is there a drainage hole in the container? What is it potted in? (soil...?) Where are you located and how often do you water? Is it receiving enough light?
Rina