  We study the family of Bethe subalgebras in the Yangian $Y(\mathfrak{g})$
parameterized by the corresponding adjoint Lie group $G$. We describe their
classical limits as subalgebras in the algebra of polynomial functions on the
formal Lie group $G_1[[t^{-1}]]$. In particular we show that, for regular
values of the parameter, these subalgebras are free polynomial algebras with
the same Poincare series as the Cartan subalgebra of the Yangian. Next, we
extend the family of Bethe subalgebras to the De Concini--Procesi wonderful
compactification $\overline{G}\supset G$ and describe the subalgebras
corresponding to generic points of any stratum in $\overline{G}$ as Bethe
subalgebras in the Yangian of the corresponding Levi subalgebra in
$\mathfrak{g}$.
