The undump is a relatively simple machine that takes advantage of borg logic.
t is a stockpile. s (both tiles) is a stockpile set to take from stockpile t. h is a hatch over open space, b is a retracting bridge over open space, and ^ is a citizens-trigger pressure plate linked to both the bridge and the hatch.
Dwarves accept stockpiling jobs from the stockpile, but upon reaching the first stockpile square, they find themselves without path to the distant stockpile square, and drop their goods. This creates a customizable quantum stockpile that preserves existing dump functionality.
Dwarves drop quite a few goods on the pressure plate rather than on the stockpile square. If you're both drawing from and delivering to the undump, dwarves can leave goods strewn throughout your fortress, as they find themselves without path earlier. Using it with food is not recommended for this reason-- you'll run into rot. Also be careful of permitting any bins or barrels, as this can lead to dwarves becoming stuck in infinite hauling loops. Of course, be aware that this structure will lead to massive amounts of cancellation spam.
Just a little bit of explanation of a few other things: because of the dropping of goods on pressure plates, your dwarves need the take-from stockpile so that they don't get into infinite hauling loops-- it gives them a reachable target for any goods that get dropped on the pressure plate. The bridge is a backup mechanism, as some slow dwarves with heavy items may move so slowly that they don't realize path is broken until after the hatch closes-- the bridge acts to extend the time that the final stockpile square is unreachable (from 100 ticks to 200 ticks).
Throughput is limited. Avoid the temptation for larger unreachable stockpiles, as this will create huge amounts of framerate slowdown. The best way to improve throughput is to make a larger take-from stockpile. That keeps many dwarves working, while keeping a steady reduction of the stockpile to the single stockpile square.
Tested as of 34.02.
You may also find a simple variation useful:
In this version, each of the bottom pressure plates (which are also all weights, citizens-trigger) is linked to the hatch immediately to its right. These hatches are over open space. The right-most pressure plate is also linked to the extra hatch-- the hatch where the reachable stockpile square used to be. This keeps dwarves using the undump consistently from left-to-right (in this orientation), and rather than stockpiling the goods, the goods are dropped to the level below (where you might want to have a stockpile set up instead). This is particularly useful when using physically isolated burrows. Notice that it's not impossible for something to go wrong-- if another creature moves closely behind, it might get dropped. I have never observed this to happen, and with proper design, it's unlikely to affect anything other than pets, but it is a theoretical risk. (It is possible to make a riskless dropping undump, but it is a much more complicated problem, and throughput rates are really really bad.)