  A three dimensional attractive Bose-Einstein Condensate (BEC) is expected to
collapse, when the number of the particles $N$ in the ground state or the
interaction strength $\lambda_0$ exceeds a critical value. We study systems of
different particle numbers and interaction strength and find that even if the
overall ground state is collapsed there is a plethora of fragmented excited
states that are still in the metastable region. Utilizing the
\emph{configuration interaction} expansion we determine the spectrum of the
ground (`yrast') and excited many-body states with definite total angular
momentum quantum numbers $0\leqslant L\leqslant N$ and $-L\leqslant
M_L\leqslant L$, and we find and examine states that survive the collapse. This
opens up the possibility of realizing a metastable system with overcritical
numbers of bosons in a ground state with angular momentum $L\neq0$. The
multi-orbital mean-field theory predictions about the existence of fragmented
metastable states with overcritical numbers of bosons are verified and
elucidated at the many-body level. The descriptions of the total angular
momentum within the mean-field and the many-body approaches are compared.
