The null domain is where only you are using the language and no one else is.
- Diary writing.
- Talking to the cat.
- Writing codes (e.g. your accounting books for income not reported to the tax authorities)
The null domain is for the language that isn’t ready for public use (like a new conlang), for when you’re studying a language outside of it’s normal range (Icelandic in Washington DC), or if you are in fact the last speaker of a rare language.
The null domain doesn’t really have a community, so in that respect, it isn’t fully a language. I would say it is a full language in the sense that it will evolve and be subject to the forces of erosion, sound shifts, etc.