Having almost cut one "arm" of a Roomba side brush, we needed a solution that restored the integrity of the brush, while still keeping it usable for its original purpose. That meant being flexible and having a form factor that doesn't prevent it from rotating when attached to the body of the Roomba. Of course first you have to remove the side brush, you'll need a Phillips screwdriver, read the documentation of your Roomba for more details.
Step 1: Doing It With Sugru
We decided to use Sugru; half a packet is enough, so if you have something else to fix at the same time as we did, just split it into half. Then try to form a protective cover over the "arm", forming a triangle that has one vertex on the middle of the arm, and the two other on the yellow central circle. Bend the edges of the triangle to form nice curves to avoid sharp angles that would catch hair while cleaning. Wait for 24 hours so that the Sugru can harden before mounting it.
Step 2: Mounting and Testing
Mount the side brush using a Phillips screwdriver, and gently rotate it by hand to test if it blocks movement. Then start a cleaning program and watch if the side brush spins normally. If it does, you're done, if not, try removing small amounts of Sugru with a sharp thin blade like an X-ACTO knife until it works properly.