  In this paper, we solve exit problems for a level-dependent L\'evy processes
which is exponentially killed with a killing intensity that depends on the
present state of the process. Moreover, we analyse the respective resolvents.
All identities are given in terms of new generalisations of scale functions
(counterparts of the scale function from the theory of L\'evy processes), which
are solutions of Volterra integral equations. Furthermore, we obtain similar
results for the reflected level-dependent L\'evy processes. The existence of
the solution of the stochastic differential equation for reflected
level-dependent L\'evy processes is also discussed. Finally, to illustrate our
result the probability of bankruptcy is obtained for an insurance risk process.
