Where is this Virasoro null from? Let's consider the Virasoro algebra with a generic $c$. Take a primary $|h\rangle$ and I try to look for its level-9 nulls: Mathematica spits out 3 solutions
$$
h = \frac{1-c}{3}, \quad \frac{1}{3}(53-5c \pm 5\sqrt{(25-c)(1-c)}) \ , \quad (*)
$$
corresponding to $h_{3,3}(c), h_{1,9}(c), h_{9,1}(c)$.
Now I consider the minimal model central charge $c = c_{p=5, p'=2} = - 22/5$ and primary $|h_{1,2}\rangle$, where as usual
$$
h_{r,s} \equiv \frac{(pr - p's)^2 - (p - p')^2}{4pp'}\ .
$$


*

*$|h_{1,2}\rangle$-module contains a null $\chi^{(1)}$ at level-$rs = 2$, with conformal weight $h(\chi^{(1)}) = h_{3,3} = h_{1,7} = \frac{ 9 }{ 5 }$, which means the $\chi^{(1)}$-submodule contains nulls at level 7 (and level 9) called $\chi^{(1,1)}$ (and $\chi^{(1,2)}$).

*I want to view $\chi^{(1,1)}$ as a level-9 null of $|h_{1,2}\rangle$-module, but this seems to fail: $h_{1,2}$ is not in the three null solutions in eq. $(*)$.

*However, if I specify $c = -22/5$ before solving the level-9 null equations, I will find the extra solution $h = -22/5$.
So my question is: what is happening as $c \to - 22/5$? Where was this extra null before setting $c=-22/5$? 
 A: The Kac determinant formula tells you that a Verma module of dimension $h$ has a null vector at level $rs$ if $h=h_{r,s}(c)$. If $c$ is generic, all null vectors are of this type. However, if $c$ is rational and in particular in minimal models, some null vectors are not of this type. A null vector of a null vector is a null vector, but it is not always of this type. You have provided an example of this phenomenon. 
In a minimal model, the Kac formula already gives infinitely many null vectors in each representation, since $h_{r+kp',s+kp}=h_{r,s}$ for any $k=1, 2, 3, \dots$. But to get all null vectors, you need to add the null vectors of null vectors.
See also Exercise 2.5 of my review article https://arxiv.org/abs/1406.4290 . 
A: Ok it turns out the rough answer is mostly simple.


*

*The additional null was of course hidden among all the level-7 nulls of $\chi^{(1)}$. It contributes to $det M^{(9)}$ inside the factor
$$
(-5 + \sqrt{(1-c)(c-25)} + c + 16 h)^{15} \xrightarrow{c \to -22/5} (h + 1/5)^{15}
$$
where $15 = \mathfrak{p}(9-2)$, the number of descendants of $\chi^{(1)}$ at this level.

*As $c \to -22/5$, one of the descendant becomes primary. The detail behavior of $c \to -cc/5$ of the null equations remain unclear (and probably not important), but I suspect it's similar to what happens to the following set of equations in the limit,
$$
  a x_1 + b x_3 = \alpha, \quad a'x_1 + b'x_3 = \beta, \\
  h x_2 + (c + \frac{ 22 }{ 5 }) x_3 = \gamma \ ,
  \quad
  h x_2 - (c + \frac{ 22 }{ 5 }) x_3 = \gamma\ ,
$$
where at $c = - 22/5$ a solution appears while in general there is no solution.
