Temperature sweeps of dynamic viscoelastic properties have shown that p-hydroxybenzoic acid (PHB)-based liquid crystalline polyesters, specifically in this case those copolymerized with poly(ethylene terephthalate) (PET), can be subjected to considerable supercooling if initial heating curves are compared to subsequent cooling curves, indicating that this type of material can be in quite different states even at the same temperature, depending on thermal history. Utilizing this supercooling behavior, viscoelastic properties of a 60 mol% PHB/40 mol% PET material produced by Unitika were monitored before and, particularly, after large-scale shear deformation to determine how potential structure changes induced by the shear are reflected in viscoelastic properties immediately, and with time. According to dynamic viscoelastic temperature sweep data four quite different initial states were employed including conditions with, as well as largely free of, crystallites. However, in all cases, post-shear monitoring showed decreased G' and G'' values with almost no evidence of return towards initial values within approximately 25 min. These results, in addition to furthering somewhat the fundamental understanding of the flow and relaxation properties of liquid crystalline polymers, may be useful in polymer processing, where large-scale shear deformations employed in forming processes appear to be capable of changing considerably the subsequent behavior of such materials.