  Exotic compact objects (ECOs) have recently become an exciting research
subject, since they are speculated to have a special response to the incident
gravitational waves (GWs) that leads to GW echoes. We show that energy carried
by GWs can easily cause the event horizon to form out of a static ECO ---
leaving no echo signals towards spatial infinity. To show this, we use the
ingoing Vaidya spacetime and take into account the back reaction due to
incoming GWs. Demanding that an ECO does not collapse into a black hole puts an
upper bound on the compactness of the ECO, at the cost of less distinct echo
signals for smaller compactness. The trade-off between echoes' detectability
and distinguishability leads to a fine tuning of ECO parameters for LIGO to
find distinct echoes. We also show that an extremely compact ECO that can
survive the gravitational collapse and give rise to GW echoes might have to
expand its surface in a non-causal way.
