That is some pretty significant damage but there is nothing that I can see that would imply that it would effect the sound in a negative way. What I would want to see is if there is any open seams on this instrument, and by the condition it is in, I could see that being a strong possibility. I would bring it in to get a checkup and possible appraisal/repair estimate.
I’m really curious how that happened. It almost seems like some sort of deterioration caused by weather in some way. Like someone left the violin in a hot place and the sides melted. That gives me cause of concern if it was weather related regarding the overall quality of the instrument. This is all speculation of course, and I think I would be able to give you more evaluation based on seeing more images. Again I’m not expert, but I did work at a string store for 3 years as a head salesman. I now would say I’m competent with minor repair and damages, but honestly I’ve never seen something like that before.