The visco-elastic properties of entangled polymer liquids arise from molecular-scale topological interactions and stochastic fluctuations under flow. Here, the evolutions of individual entangled polymers were observed in rheologically relevant shear flow histories. We uncover a high degree of molecular individualism and broad conformational distributions resulting from incessant stretch-collapse cycles. The data and insights of the present study may lead to improved molecular-level models and constitutive equations. These tools, in turn, may enable the rational design of novel materials with properties tailored to accomplish specific tasks such as high-pressure vessels and piping with greater safety margins and cost-effectiveness.