The extinction or removal of an organism from a food web can affect different organisms directly or indirectly, depending on the trophic level the organism is and in what role they play in the food web, if it is carnivore, herbivore, omnivore, etc.
Extinction has also been important for evolution in food webs. Some food webs are generated from the reaction with repeated extinctions, and the extinction rate is affected by food web structure, and food web structure is a product of previous extinctions. This means that they form a kind of cycle.
The extinction of one organism can cause a ripple effect that impacts all of the species involved in that food web. This means that one organism would destabilize the whole food web.
The extinction of a keystone specie might force all the organisms to adapt, because this specie is one whose presence and activities strongly affect other species. In other cases the ecosystem is the one that adapts to the lack of the organism. The extinction of species with a strong interaction in the food web occur more often that the others that do not have much interaction. In some cases the food web would be affected because some animals would not have a source of food, therefore they would not have energy. That way they would have to find another way to get the food or in extreme cases they could also get extinct.
An example is like the one in the picture, if the phytoplankton dies or decreases its number, its consumers would decrease their number as well, eventually the decrease of a very tiny organism would end up to the extinction of a large organism such as the killer whale or elephant seal.
In this other photo we can see different types of secondary extinction. It shows how depending on the level the extinct organism is, the food web would be affected. The thin line shows the impact only in the trophic level and the thick line shows also how