Major volcano flank collapses strongly affect the underlying magmatic plumbing system. Here, we consider the magma storage zone as a liquid pocket embedded in an elastic medium, and we perform numerical simulations in two-dimensional axisymmetric geometry as well as in three dimensions in order to evaluate the consequences of a major collapse event. We quantify the pressure decrease induced within and around a magma reservoir by a volcano flank collapse. This pressure reduction is expected to favor replenishment with less evolved magma from deeper sources. We also estimate the impact of the magma pressure decrease, together with the stress field variations around the reservoir, on the eruptive event associated with the edifice failure. We show that, for a given magma reservoir geometry, the collapse of a large strato-volcano tends to reduce the volume of the simultaneous eruption; destabilization of large edifices may even suppress magma emission, resulting in phreatic eruptions instead. This effect is greater for shallow reservoirs, and is more pronounced for spherical reservoirs than for vertically-elongated ones. It is reduced for compressible magmas containing a large amount of volatiles. Over a longer time scale, the modification of pressure conditions for dyke initiation at the chamber wall may also explain an increase in eruption rate as well as an apparent change of magma storage location.