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There's Oddly Small Organization, and take a look at some of the more specific subtropes listed there (e.g. Critical Staffing Shortage or Suspiciously Small Army...)
With This Herring comes to mind in some situations. "You are our only hope to defeat the enemy fleet. Here's an old gunboat we kind of refurbished."
Being "set up to fail" also has shades of Uriah Gambit, if someone is deliberately underequipped for the job in the hopes they'll be killed by enemy firepower.
Edited by KDReassigned to Antarctica when someone is given a new position like this to punish them or get them out of the way- say, Alice makes her senior officer Bob look bad in front of the general, so Bob is quick to recommend her when asked for candidates to head the understaffed fort in the middle of nowhere.

I got the idea from a trope ‘One-ship Navy’ currently on the launch pad. The trope covers one heroic ship doing all the work, apparently. But it got me thinking, there must be a trope somewhere that applies to the whole ‘navy’ being literally one ship, and a pretty crappy one too…
So I am looking if there is a trope already where an outfit with a real fancy title on second look turns out to be a ridiculously understaffed or under-equipped sorry excuse for a department or assignment. May be the ‘Navy Command’ you are posted to is literally just one WWII era patrol boat, or your fancy new job title entails looking over a paper archive that no one ever uses anymore along with an archivist that has been on the job since the last century. Whatever it is, if you ever had high hopes for your new command, suddenly you realized you actually have been promoted away or even set up to fail.
Anybody knows of such a trope?