We probe the onset and effect of contact changes in two-dimensional soft harmonic particle packings which are sheared quasistatically under controlled strain. First, we show that, in the majority of cases, the first contact changes correspond to the creation or breaking of contacts on a single particle, with contact breaking overwhelmingly likely for low pressures and/or small systems, and contact making and breaking equally likely for large pressures and in the thermodynamic limit. The statistics of the corresponding strains are near-Poissonian, in particular for large-enough systems. The mean characteristic strains exhibit scaling with the number of particles N and pressure P and reveal the existence of finite-size effects akin to those seen for linear response quantities [C. P. Goodrich , Phys. Rev. Lett. 109, 095704 (2012); C. P. Goodrich et al., Phys. Rev. E 90, 022138 (2014)]. Second, we show that linear response accurately predicts the strains of the first contact changes, which allows us to accurately study the scaling of the characteristic strains of making and breaking contacts separately. Both of these show finite-size scaling, and we formulate scaling arguments that are consistent with the observed behavior. Third, we probe the effect of the first contact change on the shear modulus G and show in detail how the variation of G remains smooth and bounded in the large-system-size limit: Even though contact changes occur then at vanishingly small strains, their cumulative effect, even at a fixed value of the strain, are limited, so, effectively, linear response remains well defined. Fourth, we explore multiple contact changes under shear and find strong and surprising correlations between alternating making and breaking events. Fifth, we show that by making a link with extremal statistics, our data are consistent with a very slow crossover to self-averaging with system size, so the thermodynamic limit is reached much more slowly than expected based on finite-size scaling of elastic quantities or contact breaking strains.@en