Your description makes me think of the type of antenna called a Sleeve Dipole or also referred to as a bazooka feed vertical. These types include a lower section made out of coax to carry the RF up to the feedpoint which is the splice point between the two wires. Usually, the lower coaxial section has a second coaxial outer conductor, or sleeve, which is connected at the splice point, but not at the base of the antenna. Such construction is usually hard to identify since a maker will usually cover the entire structure with heatshrink tubing, but there is usually a lower fat part and an upper skinny part, the whole thing being nearly half a wavelength long.