Protein synthesis is central to biochemical activities in a living cell. Remember that even enzymes are proteins. Interruption of protein synthesis will lead to cell death. Expression of attributes in gene is not possible without protein synthesis which is hall mark for further development of organelle and cell function. This is just a simple way to explain
Most antibacterial protein synthesis inhibitors are bacteriostatic, not bactericidal. This is true for the individual components dalfopristin and quinupristin, but when combined (as Synercid) they can be bactericidal. Both compounds bind to the ribosome at separate locations and cooperatively. From my brief reading, it seems that Synercid is only bactericidal in some cases. See here for example: Article Influence of erythromycin resistance, inoculum growth phase,...
Whether or not the drug is cidal probably depends on the physiology of the individual strain, i.e. how it responds to a profound blockage in protein synthesis.
This is the closest I could come to an explanation for the molecular mechanism of the cidality:
"Upon binding of the streptogramins, the peptidyl transferase centre undergoes a significant conformational transition, which leads to a stable, non-productive orientation of the universally conserved U2585. Mutations of this rRNA base are known to yield dominant lethal phenotypes. It seems, therefore, plausible to conclude that the conformational change within the peptidyl transferase centre is mainly responsible for the bactericidal activity of the streptogramins and the post-antibiotic inhibition of protein synthesis."
Source:Article Alterations at the peptidyl transferase centre of the riboso...