Yuka plant is half dead

Firstly Happy New year everyone and secondly help. My Yuka which I thought was the strongest of my house plants is in despair, it seems one of the trunks , the taller one has still got a lot of life in it where as the smaller one has a lot of rot through it. When I gently squeeze the bark it’s soft and spongy, also the top looks infested. So my question is should remove the dead, infested short trunk or will that be detrimental to the larger trunk ?