"How did they accomplish this?"

If this is really right (that the mean signal in one group is zero), then they simply did it wrong. Why should you want to know what kind of mistake they did? To repeat their mistake?

Apart from this: shouldn't this be described in the methods sections of these papers (possibly in the supplementary methods)?

You can do this by adding an arbitrary value to your zero values by a fraction of an intensity count. This prevents dividing by 0. E.g. you may add a 0.5 fraction intensity to all your zero values but also to your normal values you would add this too so that you are comparing 0.5 vs 200.5 which would then give you a fold change and also allow you to do stars to get a p value. I describe a fractional count as an arbitrary value to add or you can use a median/mean value. You can log transform to normalise the values as well. There are ways to do this and usually this is described in the methods of the paper you're reading.

Albert Lee : the issue with doing this is it makes the fold changes entirely arbitrary. Imagine I have a protein I detect in my test samples at "arbitrary value 10" but do not detect in my control samples at all.

If I call the ctrl value 0.5, then 0.5 vs 10.5 = 20 fold increase.

If I call the ctrl value 0.1, then 0.1 vs 10.1 = 100 fold increase.

If I call the ctrl value 0.0001, then 0.0001 vs 10.0001 = 100,000 fold increase.

In reality, the increase is effectively "infinite fold", but what this is really highlighting is that fold changes are not an appropriate metric here.

A lot (most) of statistical analysis is predicated on the measurement of change in values, not "present/absent" scenarios.

For disease biomarkers, for example, something that is present/absent is of use as a diagnostic biomarker, but not as a monitoring biomarker: you can say "if you see this marker at all, you have the disease", but you cannot really use it to track therapeutic efficacy, because all values of this marker other than "N/A" are indicative of disease.

For monitoring biomarkers you really want "healthy" and "diseased" values such that you can track the shift from one to the other.

David Genisys: I agree with Jochen Wilhelm , and would not plot my data in this manner.

A lot will depend on the kind of reviewers you get, and the type of paper you're trying to produce, but it would be more appropriate to note that these markers are entirely absent in one group, and then to comment on the robustness of their detection in the other. You wouldn't run stats necessarily, because as noted, stats are horrible for yes/no markers, but you could use the combination of presence/absence and actual level of the former to make inferences as to biological effect. If a marker goes from "not detected" to "detected but barely", then it might be indicative of dysregulated, aberrant expression behaviour, or perhaps stochastic low-level damage. Interesting, but perhaps not of biological import or diagnostic utility. If instead if goes from "not detected" to "readily detected, at high levels", then it's probably very useful as a diagnostic biomarker, and also indicative of some active biological process, be it widespread damage/release, or active expression of novel targets.

In either case you can make biological inferences without resorting to making up numbers so you can stick them on a volcano plot (and to be honest, if you get the kind of reviewers that demand volcano plots, you can always use the trick Albert suggests).

Volcano plots are primarily a way to take BIG DATA and present it in a manner that allows you to highlight the most interesting targets that have changed between groups: if you have whole swathes of genes that are instead present/absent, then those could be presented as a table, perhaps sorted by GO terms or something (if it looks like there are shared ontological categories you could use to infer underlying biology).