One of my twins died. Do I have options to protect the surviving twin?

Somewhat. When one twin dies in-utero there can be great shifts in the blood flow to the other fetus particularly if they share the same placenta. To make certain the remaining baby can hadle those shifts the baby is kept on the monitor, observed by ultrasound. If after a short time the baby looks stable then mom can go home with close follow up. As with any thing check with your provider.
Neonatologist. If they are newborns, the neonatologist needs to be consulted for this question.