"Ground" is an arbitrarily-chosen voltage convention. In space the floating ground won't cause a fault because there's never an electrical circuit with both the floating ground and the 'real' ground.
EDIT: turns out the ISS is a bit more complicated than that, and it also has a "grounding strap" that connects to the local plasma. https://news.ycombinator.com/item?id=41417136
Fun tidbit, old English cars (and the original Ford Model A!) used to tie positive DC to the frame rail as a “ground” or “common” instead of the negative DC. They are referred to as positive ground cars (and tractors!)
https://www.restore-an-old-car.com/positive-ground-cars.html
Busses also (used to?) have ground straps that you may see dragging. Apparently this was somewhat common on cars as well. "bus ground strap" is unsurprisingly difficult to search for, but I did find a discussion on Quora [1] that claims rubber formulations were responsible for vehicles picking up a static charge.
All of this is interesting once seen as an attempt to remove the potential difference between local "ground" and ambient environment.
[0] https://en.wikipedia.org/wiki/Static_wick
[1] https://www.quora.com/Cars-used-to-have-grounding-straps-han...
https://s3vi.ndc.nasa.gov/ssri-kb/static/resources/NASA-HDBK...
Apparently you attach all grounds to some common component, like the chassis and then you have a zero volt reference. As long as it is stable and the relative voltages to it are consistent, that should suffice for electrical systems. Handling overall charge of the craft might be a bigger challenge, but no idea how that would be handled.
I guess they use the same solution than during EVA which is running the Plasma Contactor Units to dissipate any buildup.
From the Commercial Crew requirements document[2]:
3.9.3.13 Integrated Space Vehicle Electrostatic Charge Control
3.9.3.13.1 LEO Charging Design Standard
The spacecraft shall meet the intent of the requirements contained in NASA-STD-4005, Low
Earth Orbit Spacecraft Charging Design Standard. [R.CTS.285]
How the contractors achieve that might be proprietary. It looks like (at one time) SpaceX used electrically conductive paint[3] as part of their mitigations.[1] https://standards.nasa.gov/standard/NASA/NASA-STD-4005
[2] https://ntrs.nasa.gov/api/citations/20150010757/downloads/20...
[3] https://phys.org/news/2013-03-white-coating-spacex-dragon-tr...
You will see that it says: "IDSS compliant mechanisms protect against electrostatic discharge through the soft capture system" which is to say not much.
That’s still more than the previous standard for which the paragraph on ESD just says "RESERVED".
[0] https://ntrs.nasa.gov/api/citations/20170001546/downloads/20...
https://ntrs.nasa.gov/api/citations/20110014828/downloads/20...
TL;DR they dissipate charge using three Plasma Contactor Units (PCUs) on the Z1 truss, and measure it using the Floating Potential Measurement Unit (FPMU) on the S1 truss. This clamps the ISS to within 20 volts of the local plasma.
https://en.wikipedia.org/wiki/Plasma_contactor
https://web.archive.org/web/20060929171819/http://space-powe...
https://www.nasa.gov/image-article/floating-potential-measur...
Any RF or EMC engineer will tell you that ground is a dirty word, especially in extreme conditions. There's no one-size-fits-all approach, since so much depends on the physical context.
[1] https://radhome.gsfc.nasa.gov/radhome/tid.htm
[2] https://www.analog.com/en/signals/thought-leadership/challen...
I would assume everything on ISS and capsules are running DC. Does DC need a ground? Every electronic circuit I've built just uses ground as the common leg to battery or power.