There is one way that shutting down electronics before a high radiation event can help protect it. It's the phenomenon called "latch up". Depending on how an integrated circuit is fabricated, there can be stray "PNPN" paths between the power rails. The PNPN structure is the same used in the "silicon controlled rectifier" (SCR), a once-common high power semiconductor device that has since been largely replaced with more modern and flexible transistor designs like power MOSFETs and IGBTs.
The main property of the SCR is that it latches. Give it just a little pulse on its gate terminal and it turns on hard. The only way to turn it off is to remove power. Normally this pulse is an external electrical signal, and since the PNPN structure is not actually desired in most ICs there is no counterpart to the gate connection in an SCR. But triggering can also come from an energetic charged particle barreling through the PNPN structure. Since most integrated circuits are not designed to withstand direct shorts across their power supplies, they can burn up very quickly, usually starting with the fine gold wires used to bond the connecting pads on the chip die to the pins of the package.
Electronics for space applications can be designed to be latchup-free, but it's not always possible to find the part you want in this flavor; you may be forced to use an off-the-shelf commercial part. In that case, you can pre-emptively shut down the circuit before you enter a high radiation environment like the SAA, and/or you can implement a "latchup detector", like a fast-acting circuit breaker, that detects the spike in supply current and interrupts it before it can do damage.