  Real projective structures on $n$-orbifolds are useful in understanding the
space of representations of discrete groups into $\mathrm{SL}(n+1, \mathbb{R})$
or $\mathrm{PGL}(n+1, \mathbb{R})$. A recent work shows that many hyperbolic
manifolds deform to manifolds with such structures not projectively equivalent
to the original ones. The purpose of this paper is to understand the structures
of ends of real projective $n$-dimensional orbifolds. In particular, these have
the radial or totally geodesic ends. In previous papers, we classified properly
convex or complete radial ends under suitable conditions. In this paper, we
will study radial ends that are convex but not properly convex nor complete
affine. The main techniques are the theory of Fried and Goldman on affine
manifolds, and a generalization of the work on Riemannian foliations by Molino,
Carri\`ere, and so on. We will show that these are quasi-joins of horospheres
and totally geodesic radial ends. These are deformations of joins of
horospheres and totally geodesic radial ends.
