  Short gamma-ray bursts (sGRBs) are thought to be produced by binary NS
mergers. While a sGRB requires a relativistic jet to break out of ejecta, the
jet may be choked and fails to produce a successful sGRB. We propose a "delayed
breakout" scenario where a late-time jet launched by a long-term engine
activity can penetrate ejecta even if a prompt jet is choked. Observationally,
such a late-time jet is supported by the long-lasting high-energy emissions in
sGRBs. Solving the jet propagation in ejecta, we show that a typical late-time
activity easily achieves the delayed breakout. This event shows not prompt
$\gamma$-rays but long-time X-ray emissions for $\sim10^{2-3}\,\rm{s}$ or even
$\sim10^{4-5}\,\rm{s}$. Some delayed events may be already detected as
soft-long GRBs without supernova signatures. In an optimistic case, a few
events coincident with gravitational-waves (GWs) are detected by the
second-generation GW detectors every year. X-ray followups of merger events
without $\gamma$-rays will be a probe of long-lasting engine activities in
binary mergers.
