Q: Serpentine belt came off of 2005 Toyota Camry

The bottom pulley is called the harmonic balancer. It helps the internals of the cars engine rotate smoothly by damping the vibrations. The pulley portion of the balancer is attached by a thick rubber glue. Over time, this glue becomes brittle and can break. When this does, the balancer stays on the engine, but the pulley portion breaks off and kicking your belt off track with it. Replacement of the balancer is the usual repair. Although it is not very complicated, it does require special tools to remove the old balancer, the bolt that holds it and to install the new balancer. I suggest seeking help form a qualified mechanic, such as one from YourMechanic, to help you verify this issue and replace your harmonic balancer if needed.