With a Dead shaft idler, bearings are installed in each end of the roller body and the shaft passes through the body of the roll. The shaft is mounted to the framework of a machine and the roll body rotates around the fixed shaft. The shaft does not rotate so it is called a dead shaft.
With a Live shaft idler, the shaft ends are rigidly fixed on each end of the roller body. When a Live shaft roller rotates the shaft ends rotate with it, so it is called a Live shaft. The bearings for a Live shaft idler are mounted on the framework of a machine and they are not part of the roller body.