Soft jammed materials can resist deformation or accommodate steady flow depending on imposed stresses and deformation rates. Designing these properties is central to a range of construction technologies and materials such as cement paste. Cessation of flow generally results in a complex stress relaxation process and finite residual stresses, and controlling these effects is especially important in additive manufacturing, In particular, even in relatively simple pastes and jammed particle suspensions, the rate of stress relaxation, as well as the magnitude of the residual stress have been shown to systematically depend on the preceding flow conditions. New insight into the mechanisms for stress relaxation, gained via microscopic simulations, highlights that flow in a broad range of yield stress fluids can be seen as a training process during which the material stores information of the flowing state through the development of domains of correlated particle displacements and the reorganization of particle packings optimized to sustain the flow. Flow cessation becomes then a way to retrieve this encoded memory. Combining simulations and experiments allows us to disentangle the role of elasticity and plasticity not only in steady flow, but also in the pre-yielding regime leading to ductile or brittle yielding and in the recovering of rigidity and mechanical stability after flow cessation.