You can have the damaged section of the trunk floor cut out, and have new steel welded in. However, your car is not an old-fashioned “body on frame” design that readily allows for simply cutting-out and replacing structural steel.
Even though a '96 vehicle never had the amount of passenger protection designed into it that more modern cars have, the fact remains that the structure of that car was very carefully designed, using the technology of the time to provide maximum passenger protection in the event of a collision.
The questions that should be asked at this point include:
Is the new steel an alloy of the exact same composition as the original steel?
Has the new steel been formed in a huge hydraulic press in the exact shape of the original steel, whose conformation was specifically designed to provide a “crush zone”?
Will the body shop guarantee that the car’s structure will perform exactly like that of a '96 Corolla that was not repaired, in the event of a crash?
Trust me–if the body shop answers your questions HONESTLY, they would have to answer “no” to at least two of those questions, and probably all three of those questions. Or–better yet–ask them to give you their assurances in writing, on their company stationery.