Take any system which has states labelled by $i$ and occupation numbers labelled by $f_i$. I.e. $f_i$ is the expectation number of particles in the given state and is normalized not to one but as $\sum_i f_i = N$. Now let this system have a probability of transition per unit time from the state $i$ to another one $j$ denoted by $P_{ij}$. This means that $f_i P_{ij}$ particles will jump to $j$ from $f_i$ in unit time. On the other hand, $f_j P_{ji}$ particles will jump from $j$ to $i$ in the same time. Hence, we can characterize the time derivative of the occupation number as

$$\frac{d f_i}{d t} = \sum_j (P_{ji} f_j - P_{ij}f_i)$$

In many systems, particularly reversible ones we have $P_{ij}=P_{ji}$.

Imagine, however, that we are dealing with identical quantum particles, there we can derive from the permutation symmetries that the transition rates have to be modified as

$$\frac{d f_i}{d t} = \sum_j [P_{ji} f_j(1\pm f_i) - P_{ij}f_i(1 \pm f_j)]$$

where the plus is for Bose statistics and the minus for Fermi statistics. In particular, you can see that for fermions the probability of transition from $j$ to $i$ is zero if the state is already occupied.

The specific case of a gas in astrophysics can be modelled by the Boltzmann equation

$$\partial_t f + \partial_p H \partial_x f - \partial_x H \partial_p f = \delta f_{coll}$$

where $f(p,x)$ now stands for the occupation number in a phase-space cell of volume $\sim \hbar$ at $p,x$, and $H$ is some effective single-particle Hamiltonian which represents the free drifting of the microscopic particles in the macroscopic fields. The right-hand side is the collision term which (within a certain approximation) modulates the behaviour of the occupation number due to collision between particles.

Particles following Boltzmann statistics would have

$ \delta f_{coll}(p,x) = \int Q(p,q \to p',q') [f(p,x) f(q,x)- f(p',x)f(q',x) ] dq' dq dp'$

where $Q(p,q \to p',q')$ is a scattering matrix computed for two particles scattering off each other while being alone in the universe. However, in analogy with the previous part of this answer, fermionic particles have

$\delta f_{coll}(p,x) = \int Q(p,q \to p',q')$

$\left[ f(p) f(q)(1-f(p'))(1-f(q')) - f(p')f(q')(1-f(p))(1-f(q)) \right] dq' dq dp'$

where I have written $f(q,x) \to f(q)$ for brevity.

I.e., the probability of scattering into a state occupied with density $f(p,x)$ will be modulated by a $1-f$ factor. If $f$ is close to one, this scattering will be essentially forbidden. In strongly degenerate gases this means that we can essentially neglect *any* scattering outcome in the Fermi phase-space surface, be it elastic or non-elastic.