  We study entry loci of varieties and their irreducibility from the
perspective of $X$-ranks with respect to a projective variety $X$. These loci
are the closures of the points that appear in an $X$-rank decomposition of a
general point in the ambient space. We look at entry loci of low degree normal
surfaces in $\mathbb P^4$ using Segre points of curves; the smooth case was
classically studied by Franchetta. We introduce a class of varieties whose
generic rank coincides with the one of its general entry locus, and show that
any smooth and irreducible projective variety admits an embedding with this
property.
