  We construct a piecewise model that gives a physical viable realization of
finite-time future singularity for a spatially flat Friedmann-Robertson-Walker
universe within the interacting dark matter--dark energy framework, with the
latter one in the form of a variable vacuum energy. The scale factor solutions
provided by the model are accommodated in several branches defined in four
regions delimited by the scale factor and the effective energy density. A
branch starts from a big bang singularity and describes an expanding
matter-dominated universe until the sudden future singularity occurs. Then, an
expanding branch emerges from a past singularity, reaches a maximum, reverses
its expansion and possibly collapses into itself while another expanding branch
emerges from the latter singularity and has a stable de Sitter phase which is
intrinsically stable. We obtain a different piecewise scale factor which
describes a contracting de Sitter universe in the distant past until the
finite-time future singularity happens. It emerges and continues in a
contracting phase, bounces at the minimum, reverses, and enters into a stable
de Sitter phase without a dramatic final. Also, we explore the aforesaid cosmic
scenarios by focusing on the leading contributions of some physical quantities
near the sudden future singularity and applying the geometric Tipler and
Kr\'olak criteria in order to inspect the behavior of timelike geodesic curves
around such singularity.
