  The composite cosmological objects -- Kibble-Lazarides-Shafi (KLS) walls
bounded by strings and cosmic strings terminated by Nambu monopoles -- could be
produced during the phase transitions in the early Universe. Recent experiments
in superfluid $^3$He reproduced the formation of the KLS domain walls, which
opened the new arena for the detailed study of those objects in human
controlled system with different characteristic lengths. These composite
defects are formed by two successive symmetry breaking phase transitions. In
the first transition the strings are formed, then in the second transition the
string becomes the termination line of the KLS wall. In the same manner, in the
first transition monopoles are formed, and then in the second transition these
monopoles become the termination points of strings. Here we show that in the
vicinity of the second transition the composite defects can be described by
relative homotopy groups. This is because there are two well separated length
scales involved, which give rise to two different classes of the degenerate
vacuum states, $R_1$ and $R_2$, and the composite objects correspond to the
nontrivial elements of the group $\pi_n(R_1,R_2)$. We discuss this on example
of the so-called polar distorted B phase, which is formed in the two-step phase
transition in liquid $^3$He distorted by aerogel. In this system the string
monopoles terminate spin vortices with even winding number, while KLS string
walls terminate on half quantum vortices. In the presence of magnetic field,
vortex-skyrmions are formed, and the string monopole transforms to the nexus.
We also discuss the integer-valued topological invariants of those objects. Our
consideration can be applied to the composite defects in other condensed matter
and cosmological systems.
