The present invention is a new liner assembly for use in pipes constructed from a flexible liner formed from a resin absorbent material. A compressible material, such as stitch-bond or foam, is attached to one or more sides of the liner for forming a taper along the compressible material when the liner is cured in place in the pipe using a curable resin and an expandable bladder to shape the liner to match the inside shape of the pipe. A taper is formed along the compressible material from the inside of the liner down to the inside of the pipe in which the liner is placed. As a result, a taper prevents accumulation of solid materials at the location of the pipe repair and thus prevents future clogging of the pipe at the repair.