it is probably more meaningful to talk about dN/dS for a branch on the species phylogeny than dN/dS for a species. Even so, the estimates may have very large sampling errors if the branch is short. I think if you have a few thousand genes, and concatenate them into one supergene, you will have many sites (codons), and then the free-ratios model will be able to estimate dN/dS for each branch with high precision, and the estimates can be interpreted as genome-wide averages. Such estimates make some intuitive sense but may not be very useful.
999 is the upper limit set by the program, and means infinity. If you apply the free-ratios model to each gene, with only 200 or 500 codons, and if no synonymous substitutions have occurred on a short branch, then the program will give you an estimate of infinity. Similarly if no nonsynonymous substitutions have occurred on a short branch, you will get 0 (0.0004, the lower bound set by the program), which is also an extreme estimate.
The situation is like flipping a coin twice and getting two heads, and the MLE of probability of heads will be 100%, which is extreme.
ziheng