  We show that the BPS property is a generic feature of field theories in (1+1)
dimensions, which does not put any restriction on the action. Here, by BPS
solutions we understand static solutions which i) obey a lower-order
Bogomolny-type equation in addition to the Euler-Lagrange equation, ii) have an
energy which only depends on a topological charge and the global properties of
the fields, but not on the local behaviour (coordinate dependence) of the
solution, and iii) have zero pressure density. Concretely, to accomplish this
program we study the existence of BPS solutions in field theories where the
action functional (or energy functional) depends on higher than first
derivatives of the fields. We find that that the existence of BPS solutions is
a rather generic property of these higher-derivative scalar field theories.
Hence, the BPS property in 1+1 dimensions can be extended not only to an
arbitrary number of scalar fields and k-deformed models, but also to any (well
behaved) higher derivative theory. We also investigate the possibility to
destroy the BPS property by adding an impurity which breaks the translational
symmetry. Further, we find that there is a particular impurity-field coupling
which still preserves {\it one-half} of the BPS-ness. An example of such a BPS
kink-impurity bound state is provided.
