Ultimately all advanced electronics will end up like this. Perhaps a clever fabricator can machine a new engine block - but one-off microchips are simply not a thing
Custom digital logic chips can be fabricated using complex programmable logic devices (CPLDs) and field-programmable gate arrays (FPGAs); these are commonly used when developing and prototyping new systems. We're even getting to the point where some adventurous people have managed to set up basic silicon fabrication plants in their (large) garages!
A greater issue is working out what it is you're trying to replicate, especially if documentation is lacking. While black-box methods (what outputs do you get for particular combinations of inputs) and knowledge of the rest of the system can get you so far, but some mysteries may remain, especially with undocumented "features" .
For the ultimate in reverse engineering, some enterprising individuals crack open microchips, etch away plastic coatings with acid, and grind off tiny layers of the microchip's die, photographing it layer-by-layer with a camera attached to a microscope. This can be achieved by a skilled enthusiast with a well-equipped workshop/shed for top-end chips designed in the 70s and 80s.
Having obtained a good set of die scans, it's possible to visually identify transistors and connections within the die, and reverse-engineer the chip's design from the ground up. Any areas of ROM or microcode (e.g in a microcontroller) can be read out as a grid of present/absent connections representing ones and zeroes, often revealing missing or undocumented instructions. This latter step is often best crowdsourced to a number of electronics enthusiasts, rather than leaving it to the single guy with a microscope.
This is a destructive process, but by sacrificing one chip you can work out exactly what and how it does, and get the information you need to reimplement it yourself.