What will happen if a producer is eliminated from the food chain?

All the components of the food chain are integrally connected to each other and modification at any level impacts all the other levels as well. The food chain consists of producers (such as plants), primary consumers (typically herbivores, such as deer, etc.), secondary consumers (typically carnivores, such as lion, etc.), etc. If any one of these is added or removed from the food chain, the entire chain will be affected. For example, if a producer is removed from the food chain, there would be less food available for the primary consumers, such as deer. This will result in a lower population of primary consumers or herbivores. This effect will also reflect in the population of carnivores, due to decreased amount of food. Reduced carnivore population will, in turn, require less food and herbivore population will ultimately stabilize to a new equilibrium. 

In the end, a new equilibrium (between various food chain components) will be established (assuming the removed producer was one of the many producers).

Hope this helps.