  In the classical stochastic resetting problem, a particle, moving according
to some stochastic dynamics, undergoes random interruptions that bring it to a
selected domain, and then, the process recommences. Hitherto, the resetting
mechanism has been introduced as a symmetric reset about the preferred
location. However, in nature, there are several instances where a system can
only reset from certain directions, e.g., catastrophic events. Motivated by
this, we consider a continuous stochastic process on the positive real line.
The process is interrupted at random times occurring at a constant rate, and
then, the former relocates to a value only if the current one exceeds a
threshold; otherwise, it follows the trajectory defined by the underlying
process without resetting. We present a general framework to obtain the exact
non-equilibrium steady state of the system and the mean first passage time for
the system to reach the origin. Employing this framework, we obtain the
explicit solutions for two different model systems. Some of the classical
results found in symmetric resetting such as the existence of an optimal
resetting, are strongly modified. Finally, numerical simulations have been
performed to verify the analytical findings, showing an excellent agreement.
