  We prove that every separable tracial von Neumann algebra embeds into a
II$_1$ factor with property (T) which can be taken to have trivial outer
automorphism and fundamental groups. We also establish an analogous result for
the trivial extension over a non-atomic probability space of every countable
p.m.p. equivalence relation. These results are obtained by using the class of
wreath-like product groups introduced recently in \cite{CIOS21}.
