I think this situation requires case-specific analysis. Log2(0) is -Inf, so the fold-change value is unhelpful but not unexpected. In some cases the gene is genuinely expressed only in one condition. That is unusual but could be extremely interesting, so I would not arbitrarily dump these genes. However, if your samples say "not expressed and just barely only a tiny little bit expressed" then I think it is like that the sample showing extremely modest expression is a false positive. Cases where one condition shows robust expression and the other shows lack of expression may be better true positive candidates. Cases where replicates show the same behavior are much more interesting. Look at the reads in IGV or a pileup. Beware of confounding biases that co-vary with your differential expression analysis.