  The first goal of this article is to investigate a refinement of
previously-introduced strongly regular hyperbolic automorphisms of locally
finite thick Euclidean buildings $\Delta$ of finite Coxeter system $(W,S)$. The
new ones are defined for each proper subset $I \subsetneq S$ and called
strongly $I$-regular hyperbolic automorphisms of $\Delta$. Generalizing
previous results, we show that such elements exist in any group $G$ acting
cocompactly and by automorphisms on $\Delta$. Although the dynamics of strongly
$I$-regular hyperbolic elements $\gamma$ on the spherical building
$\partial_\infty \Delta$ of $\Delta$ is much more complicated than for the
strongly regular ones, the $\lim\limits_{n\to \infty} \gamma^{n}(\xi)$ still
exists in $\partial_\infty \Delta$ for ideal points $\xi \in \partial_\infty
\Delta$ that satisfy certain assumptions. An important role in this business is
played by the cone topology on $\Delta \cup \partial_\infty \Delta$ and the
projection of specific residues of $\partial_\infty \Delta$ on the ideal
boundary of $Min(\gamma)$.
  All the above research is performed in order to achieve the second, and main,
goal of the article. Namely, we prove that for closed groups $G$ with a
type-preserving and strongly transitive action by automorphisms on $\Delta$,
the Chabauty limits of certain closed subgroups of $G$ contain as a normal
subgroup the entire unipotent radical of concrete parabolic subgroups of $G$.
