Since the early days of ultracold atomic physics, the phenomena of matter wave collapse, i.e. unrestricted contraction of the Bose-Einstein condensate (BEC) with attractive interatomic interactions, has been studied both experimentally  and theoretically . In particular, it has been shown that a dynamically stable BEC can exist both in 3D and 2D (strongly anisotropic, pancake) harmonic traps, as long as the number of particles in the condensate is below a certain critical value. Naturally, the problem of collapse control and possible suppression in such systems is of a great fundamental and practical importance. In particular, it was suggested that for anisotropic (i.e. elliptic) two-dimensional condensate clouds carrying angular momentum the collapse can be completely arrested . Similar problem was recently analyzed in the context of nonlinear optics, where it was shown  that imprinting twisted phase front and thereby transferring an orbital angular momentum (OAM) onto light beams with elliptic cross-section allows to suppress their collapse. Although the rotating BEC with attractive interaction was studied in context of vortex formation, the fundamental role of OAM in the collapse dynamics of trapped BECs remains an open problem.