Answer:
It's difficult to define exactly how the wildlife would be affected. Different variables would affect the ultimate outcome in a situation such as this.
For example, if the plant species which becomes extinct is a species commonly used by an insect group for breeding or feeding, and in turn, these insects turn out to be a source of food for another group of animals then obviously, as the plant species becomes scarce, so would the insects, and then, without a sustained food-source, each animal group relying on the plant would dwindle in size.
This could have effects such as behavioral changes in animals, animal groups dying, as well as changes in the other plants, if along this chain, one of the groups is responsible for harvesting certain leaves from trees etc.