  Consider a sequence of Poisson point processes of non-trivial loops with
certain intensity measures $(\mu^{(n)})_n$, where each $\mu^{(n)}$ is
explicitly determined by transition probabilities $p^{(n)}$ of a random walk on
a finite state space $V^{(n)}$ together with an additional killing parameter
$c^{(n)}=e^{-a\cdot\sharp V^{(n)}+o(\sharp V^{(n)})}$. We are interested in
asymptotic behavior of typical loops. Under general assumptions, we study the
asymptotics of the length of a loop sampled from the normalized intensity
measure $\bar{\mu}^{(n)}$ as $n\rightarrow\infty$. A typical loop is small for
$a=0$ and extremely large for $a=\infty$. For $a=(0,\infty)$, we observe both
small and extremely large loops. We obtain explicit formulas for the
asymptotics of the mass of intensity measures, the asymptotics of the
proportion of big loops, limit results on the number of vertices (with
multiplicity) visited by a loop sampled from $\bar{\mu}^{(n)}$. We verify our
general assumptions for random walk loop soups on discrete tori and truncated
regular trees. Finally, we consider random walk loop soups on complete graphs.
Here, our general assumptions are violated. In this case, we observe different
asymptotic behavior of the length of a typical loop.
