Safe Mode
Tweaks run inside other people's processes, including ones the desktop depends on. Safe Mode exists because a tweak that crashes the wrong process can leave a Mac that cannot be logged into.
It turns itself on
You do not have to reach it. TweakInject watches Dock, Finder, WindowServer and the wallpaper extensions, and if one of them crashes, Safe Mode engages on its own. Those are the processes that, when they go down, take the desktop with them, so the recovery cannot depend on you being able to click anything.
A crash caused by something other than a tweak trips it too. That is deliberate: the cost of standing tweaks down unnecessarily is small, and the cost of not doing it when it mattered is a Mac you cannot log into.
Restarting the desktop yourself does not trip it. Safe Mode can tell the difference between a process being killed on purpose and one falling over.
What it does
With Safe Mode engaged, the loader stands every tweak down at process spawn. Nothing is uninstalled and no filter is changed; tweaks are simply not injected. Processes started while it is on run clean.
Turning it on and off yourself
Use the buttons in the app. They exist because the alternative is typing commands into a terminal on a machine that may not have a usable desktop, which is exactly the situation Safe Mode is for.
Clearing the flag is not enough on its own. Every process running at that moment started with tweaks stood down, so they stay untweaked until they restart. A userspace reboot is what brings everything back up with tweaks active.
Safe Mode or suspend injection?
Both stop new processes picking up tweaks. The difference is who decides. Safe Mode is automatic and exists for recovery: it arms itself and trips without you. Suspending injection is a switch you throw when you want tweaks out of the way for a while.