  Using the Birmanexact sequence for pure mapping class groups, we construct a
universal Cannon--Thurston map onto the boundary of a curve complex for a
surface with punctures we call surviving curve complex. Along the way we prove
hyperbolicity of this complex and identify its boundary as a space of
laminations. As a corollary we obtain a universal Cannon--Thurston map to the
boundary of the ordinary curve complex, extending earlier work of the second
author with Mj and Schleimer.
