An analysis of toroidal plasma compression by a collapsing flux conserver reveals linearly stable scenarios of operation to high compression ratios. The resistive and ideal MHD stability is calculated in full toroidal geometry using the asymptotic matching method in realistic conditions. A time dependent MHD simulation of the compression is conducted to confirm the conservation principles used to calculate the equilibrium states for the analysis. The near edge current profile, controlled by toroidal field ramping during compression, is shown to be critical to stability due to coupling between poloidal components of the least stable mode. Two cases with slight differences in edge current are examined, one with a stable corridor to high compression and one without.