I presume you mean Gunnera ? If so, yes eventually they would die down and eventually rot and go back into the soil.

Far better to cut them down and cover the crowns with the leaves and use the stalks to weigh the leaves down

I cut my Gunnera leaves today and covered the crown with them.

I also cover the crown with the Gunnera leaves, and it has survived very well in our central-UK winters.

I cover the crown with the Gunnera leaves as well as everyone above has said. They survive cold weather by being dry in the crown.