Absence of evidence cannot on its own be evidence of absence. However it can be evidence of absence when combined with other evidence.
For example: Say I am trying to prove that I did not take a flight. If I first demonstrate that it is the regular practice of airlines to record the names of every individual flying on a given flight, I can then prove I did not take the flight because there is no record with the airline of me on the flight. In other words, the absence of evidence of me being on the flight becomes evidence of my absence from the flight.