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I thought I understood how the rule worked about units destroyed while low on supply. My previous understanding was that if a unit is below 5 supply then when destroyed it can be rebuilt at full price, but if at 6 supply or above it can be rebuilt for a reduce price.

I also thought that the supply is the value that the unit has at the beginning of the opponent turn.

So for example if I have a Soviet unit in a city and it starts the German turn with 6 supply then the German moves 6 units around the city and attacks with them all to destroy the unit, the unit can be rebuilt for reduced cost. However, if the German moves the units around the city and waits. Then the allies get a move then on the next turn the Germans will see the supply of the city and the unit reduced to 5 (since city was cut off) and can attack the unit and kill it causing it to be rebuilt for full price (not reduced price).

Is this accurate? Or am I missing something?

I saw in a recent game the Germans surround units that I thought had 6+ supply and kill them after surrounding in the same turn and the units didn't show up to be rebuilt at reduced price. How does this happen? Any idea?

Also what is the purple shading on the hex in this picture? Why does a hex get this purple shade?

LS means less than 5, you're right. At least some units cannot be rebuilt, like light tanks, recon units and such. Additionally in case the force pool is overextended for some reason, you won`t be able to rebuild units unless you reached an account below the limit. Afaik the destroyed unit is shown nevertheless (in case of more than 4 supply).

The purple shade means an aircraft not detached to the nearest HQ.

ORIGINAL: Sugar
LS means less than 5, you're right. At least some units cannot be rebuilt, like light tanks, recon units and such. Additionally in case the force pool is overextended for some reason, you won`t be able to rebuild units unless you reached an account below the limit. Afaik the destroyed unit is shown nevertheless (in case of more than 4 supply).
The purple shade means an aircraft not detached to the nearest HQ.

Thanks but that's not my question really. I think you are answering about whether units are re-buildable at all.

What I'm asking about is when units can be rebuilt at a reduced cost. They have an asterisk (*) next to them on the build list to show they are discounted (cheaper). When is that the case and when not?

5.24. Military Production
Land and air units that were destroyed in
combat while they had a supply value of 5 or
more can be repurchased at reduced cost and
with a shorter Production Delay.

I'm not sure if they need to be able to trace back to a supply source at the time of their destruction too.

That is, to address your question about a unit that starts the turn at supply 5 or better, but is cut off and then destroyed.