  There is growing evidence that a clear distinction between magnetars and
radio pulsars may not exist, implying the population of neutron stars that
exhibit both radio pulsations and bursting activities could be potentially
large. In this situation, new insights into the burst mechanism could be gained
by combining the temporal behavior of radio pulsations. We present a general
model for radio suppression by relativistic $e^{\pm}$ plasma outflows at the
onset of magnetar flares. A sudden ejection of magnetic energy into the
magnetosphere would generate a fireball plasma, which is promptly driven to
expand at relativistic speed. This would make the plasma cutoff frequency
significantly higher than the rest frame radio frequency, resulting in the
suppression of radio waves. We analytically show that any GHz radio emission
arising from the magnetosphere is suppressed for $\sim100\ {\rm s}$, depending
on the total fireball energy. On the other hand, thermal radiation is expected
from the hot spot(s) on the stellar surface created by an inflow of dense
plasma, which could be the origin of short bursts. Since our hypothesis
predicts radio suppression in coincidence with short bursts, this could be an
indirect method to constrain the occurrence rate of short bursts at the faint
end that remain undetected by X-ray detectors. Furthermore, ultra-fast
gamma-ray flashes from the fireball photosphere is also expected as a smoking
gun, although the onboard detection is challenging due to its extremely short
duration $\sim\mu$s. Finally, our model is applied to the radio pulsar with
magnetar-like activities, PSR J1119-6127 in light of recent observations.
Implications for fast radio bursts and the possibility of plasma lensing are
also discussed.
