Why do I obtain very strange results with DESeq2?
I'm guessing here, but I suspect this is at least in part due to the fact that all your samples in condition 1 are not expressed at all. 

Formally you have an infinitely large fold-change between condition1 and condition2. Most tools solve this by adding a small pseudocount to unexpressed samples, but this will still result in a very high fold change. So far for the big fold-change.

If I had to guess at the reason why this is significant I would think in terms of dispersion estimation. This Bioconductor post has some discussion with the authors of DESeq2 on how this works.

Finally: calculating differential expression on these genes in these samples will never be really informative, as they really are only expressed in one sample. The way I see it you have two options:


Exclude the sample from your analysis. Straightforward, but does not solve this problem for other samples.
Filter your genes before calculating differential expression, i.e. remove all genes that are not expressed in a large number of samples. This approach is standard in for instance sleuth. A good starting point would be to remove genes that are not expressed in 75% of your samples.