Polymerization processes for producing ethylene-based plastomers and elastomers having densities less than 0.91 g/cm3 utilize a metallocene-based catalyst system containing a chemically-treated solid oxide. These polymerization processes can be conducted in a slurry reactor, a solution reactor, and/or a gas phase reactor. Ethylene polymers produced from the polymerization process can be characterized by a density of less than 0.91 g/cm3, a CY-a parameter of less than 0.2, and a ratio of HLMI/MI of at least 30, or a density less than 0.91 g/cm3, a CY-a parameter from 0.25 to 0.75, and a ratio of Mw/Mn from 2 to 3.