What are you talking about? That's absolutely not the case for ticks. And for mosquitos it's often doubtful at best, and false when it comes to disease carrying species as there are plenty of other species available.
Sure. And those wasps maybe has other parasitic wasps, and those parasit wasps maybe have flees, who have bacterial diseases, who have viral diseases. All of them parasitic and all who would go extinct when that species goes extinct.
But that's not what the previous poster was talking about. This is not the basis of a food web, that's just a parasitic cul de sac. And there are basically infinite such things in nature.
"Will eat" and is the "base of a food web" are radically different things. Humans "will eat" pistachios, but the eradication of pistachios will do absolutely nothing to the human species.