Let $G$ be a countable discrete group and $\mathrm{Sub}(G)$ be the set of all its subgroups which be can be topologized by viewing $\mathrm{Sub}(G)$ as a (closed) subset of $\{0,1\}^G$. Let $G$ act on $\mathrm{Sub}(G)$ by conjugation. An invariant random subgroup (IRS) of $G$ is a Borel probability measure on $\mathrm{Sub}(G)$ which is invariant under the action of $G$. A trivial example is the dirac measure $\delta_N$, where $N$ is a normal subgroup. Another source of examples comes from probability measure preserving actions of $G$; that is, let $G$ act on a standard probability space $(X,\mu)$ in a measure preserving way. The map $x\to \mathrm{Stab}_x$ from $X$ to $\mathrm{Sub}(G)$ is measurable and we may consider the pushforward of $\mu$ to $\mathrm{Sub}(G)$ which is then an IRS.
It is a result of Abert, Glasner and Virag that actually every IRS on $G$ arises in this way.
My question is: For a given normal subgroup $N$ of $G$, is there some simple pmp action of $G$ such that the corresponding IRS is $\delta_N$? I mean, I would like to avoid the general result mentioned above (from https://arxiv.org/pdf/1201.3399.pdf Proposition 13) if possible and find more directly some pmp action giving the trivial IRS.
I would also appreciate a reference, if such exists, to where the result of Abert, Glasner, Virag is proved more in detail as I found their proof too sketchy and difficult to understand.