Alright, so the primary inspiration for this is 55 Cancri e, the speculated carbon "diamond world" and to a degree, Nkllon, a planet in Star Wars that is essentially what Cancri is, but "confirmed" to be a crystal mineral-rich planet in-world. I gave Nkllon as an example because it bears many similarities with Cancri as both are uninhabitable carbon-based planets extremely close to their parent star, making it very, very inaccessible. To reach Nkllon, the use of shield ships were employed, which were umbrella-like vessels that could resist the extreme rays and heat.
Now, I don't want to rip off Star Wars (even though the planet bears many is "essentially" Cancri e. So to mediate this, I was thinking about making the star a white dwarf rather than basing it off the star similar to our own. White dwarfs are formed by stars less than a quarter mass of our sun, so they immediately shrink without undergoing the process of becoming red giants, expanding and consuming the planet (since they're at such a close range) in the process before finally becoming a dwarves. The problem with this is that I don't know if a star the quarter mass of ours is even capable of providing the correct conditions to go about producing such rare materials in its system.
If that's the case, and a white dwarf is truly incapable of allowing such, could any other astronomical body while in conjunction with the white dwarf allow this planet to form?