The default Arduino Core does not keep the EIC clock running when entering deep sleep. This means that any change interrupt will not be detected correctly (CHANGE, RISING or FALLING). HIGH or LOW can still be detected without an active clock.
There isn't really any possibility of detecting change interrupts without an active clock signal. However, in the example I provide it is the XOSC32K which is kept active. This isn't very expensive with regards to power.