This seems to be a feature request as per comment #0. Hence, marking it as untriaged for further inputs from dev team.

Thanks...!!

Does not look like a high demand feature.
What the path should be relative to?
Could you please describe exact use cases?

Undoubtedly not a high demand feature, as I said in the Google thread it would likely be of the most use for developers who are performing data-related tasks with URLs, and considering how developers often work in staging/dev areas and push to live, ultimately they would want to use a relative address in most cases. 

E.g. let's say you are running a car dealership website and need to manually go through the entire inventory and update a field that contains a unique link to another part of that website. Instead of, going one by one, right-clicking the links > copy link address, pasting into the field, removing the absolute domain information, you could remove one of those steps.

I fully understand this is definitively not a high priority type of thing, but having just had to do something like that for a large amount of links, I couldn't help but think this would be a nice-to-have to shave off a step in a tedious process. Certainly just a QOL thing, though.

Archived = old bug with no activity.

Archived isn't the right status for this bug. Can't tell if closing it as Archived was a mistake or not. If Chromium decides not to implement this, they could close it as WontFix - but I do think that this could be a useful (but not high-demand) feature at times. Or, perhaps, would something like this be the job of an extension?

I think it was a mistake to close this bug as Archived. Could someone correct the status to Assigned if that was what was intended?