The question is perhaps a bit malformed. The question might better be asked 'When is the absence of evidence evidence of absence?'.
If we can encapsulate our search space and make it discrete and give clear and objective test for the evidence or lack thereof within a given space, it would make sense to consider the absence of evidence as evidence of absence. The simplest example is looking for shoes in your closet. If the closet is otherwise empty and free from visual obstruction a perusal of the entire space in the closet should be sufficient to take the absence of evidence (the shoes that are sought are not visible there) as evidence that they do not exist in the closet.
Two objections to be raised: (a) this is evidence of absence in as much as the perusal of the closet generates evidence and (b) in a larger search space the issue of parallel search presents itself as, in a serial search, it is possible that the object of the search has moved from one area 'to be searched' to a location 'already searched', frustrating the search operation.
That is basically begging the question by saying that absence of evidence is evidence of absence. That is the same as trying to prove something by claiming it. For example, if I wanted to prove that global warming is a hoax and I start out by saying global warming is a hoax. It is the same reasoning.
This only shows that the evidence hasn't been discovered yet. The evidence itself is absent, but not necessarily because the object, person, theory, or thing that should be supported by evidence is absent, only because the evidence is absent. Does that make sense? It doesn't prove that something is absent at all.
I mean, at first glance, it certainly seems like it is. If there is an absence of evidence, you would think that would be evidence of absence. But, that's just too simple. You have to think a little deeper and you'll find that that is not always the case. Sometimes it is, but not always.
Couldn't help myself. Anyway, no, while it may be a guiding principle to coming to a conclusion, not every scenario can be broken down as "well I don't see it, therefore it doesn't exist." Things are rarely that simple, thinking that way will more often than not make you end up looking stupid.