You're right, the JIT system falls flat on its arse if food is still going out the front door but not coming in the back door, and the stores would be stripped in a short space of time if that were to happen.
What tppb could easily do though is to close the front doors of the stores either completely or by introducing rationing, and also control the deliveries the RDC's. Each RDC may service hundreds of stores so although they too work on a JIT principle, at any one time each RDC is full of stock as everything that gets delivered to the stores is replenished though their own back door.
I cant find an edit button so before anyone thinks i've invented a new list of abbreviations

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"tppb" should read "tptb", and .... "and also control the deliveries the RDC's" should read "and also control the deliveries
from the RDC's"