If you are expecting to have a final value of '1' for example, you can design a counter that counts clock cycles during '1' .. if the counter, say, reaches a specific large value like 10 or 20 (as you decide), then you can consider the circuit is no more switching and this '1' is the final value ..
you need to have a condition for the last edge .. how will you know that it's the last edge unless you monitor it for some time and you notice that it doesn't change !! ..
If you are going to do so, then you can easily know the time at which the last edge occurs by translating the counter counts (or the number of clock cycles involved) into time .. as easy as this.