  We study the notion of non-trivial elementary embeddings $j : V \rightarrow
V$ under the assumption that $V$ satisfies $ZFC$ without Power Set but with the
Collection Scheme. We show that no such embedding can exist under the
additional assumption that it is cofinal and either $V_{\textrm{crit}(j)}$ is a
set or that the Dependent Choice Schemes holds. We then study failures of
instances of collection in symmetric submodels of class forcings.
