I want to start by saying I have zero combat experience (thankfully) and that I have only played a handful of rules so my experience of suppression and what it means is based upon very limited exposure from various sources.
In my rules, suppression acts to make infantry less likely to do what you want them to.
So for example a squad of infantry that wants to ‘advance’ would normally need a 3+, to ‘take cover’ they would need a 1+, to attach bayonets and ‘assault’ the enemy, a 4+.
However if ‘shaken’ these numbers are modified, so that advance becomes 4+, take cover 2+ and assault 5+.
Being shaken makes things harder.
Units become shaken if they take fire but pass their saves.
It is figured that the fire either panics them, causes them to be hesitant, etc., hence the negative modifiers to their command rolls.
It can also be assumed if you wish, that infantry are hit but not killed, so shaken could mean that Steve was hit and the squad gets a shaken token and the associated -1, as they are busy kneeling on Steve to stop him bleeding out.
Once a shaken squad loses a man, they also lose the shaken token.
Maybe Steve is now dead and not tying them up and they are free to act again?
Maybe they took cover and patched Steve up and are ok to go?
To lose the shaken marker they either have to lose a man or pass a command roll.
Passing command rolls depends on what order you give them.
Giving shaken troops the advance order would be 4+, giving them assault would be 5+, giving them take cover would be 2+.
So you can see that troops under fire are encouraged to be commanded in a way that would likely keep them safe.
The rules are very light and very abstract.
They are trying to balance what could happen, with what players want to happen, with a simple quick mechanic with quick play.
For me, this works…