Sony have a big infrastructure and need to salvage what they can. They will survive, but the main thing is their reputation as the leaked emails show how the executives think and even though they were private, it makes relations difficult. The company will have to be more careful about their security, but people still trust the brand, which is the important thing.
Sony has a long history of success so it is unlikely to disappear. It is more likely that it will change its direction to get back on track. The company has many resources to draw on in order to overcome financial setbacks. Sony devices and electronics remain very popular as well.
Sony will respond because they have been a household name for two decades. Their products may be faultering but their name is an electronic staple. Due to their easily recognizable trademark, and their stronghold on movie productions, the company will be successful for a long time to come. They just need better engineers to reinvent their products and concepts in a more modern way.
Sony can rebound from the recent issues if they come up with the right solution. It might take a lot of work, and quite a bit of time to rebound their finances. I think if they have some patience and some people who can think well and creatively they should be fine.