For the sake of this question I'll use the word Linux as an example, but I really want to ask about the principle generally.
The word Linux started as the name of an operating system kernel written by Linus Torvalds. The name is a contraction of a previous operating and the author's name.
In language the word is commonly use as an adjective. Eg:
Linux system
or
Linux machine
There's a subtlety here that a term like "Linux system" doesn't just refer to systems from a specific vendor in the way you might expect with "Ford car". It is often used to refer to systems with specific behaviour. Though that use may be technically incorrect - this is a language question not a technical one.
This has got me wondering what the rules are around when (if ever) the capitalisation should change from "Linux" to "linux".
Similarly I'm interested in other transitions such as English people will use a phrase
hoover the carpet
to mean cleaning a carpet with any vacuum cleaner, not just one from the brand Hoover.
There's clearly a tipping point at which the original proper noun becomes lost and only the other uses remain. However I was wondering if it's permissible before that to begin to use lower case instead of upper case.