Whatever the engineers decided to do here
It’s ironic that the booklet tucked away into the seat’s back pocket says “Safe,” because even though we know nothing about planes, covering broken glass with cardboard is not going to keep an aircraft and its passengers safe when flying a million miles above the ground. What’s also surprising is the passenger’s nonchalance of the situation.
If this were us, we’d be panicking up a storm and raising enough hell to get the pilot’s attention. However, you need to learn to put your trust in the hands of engineers, whether they’re certified and have multiple degrees or just some random guy who uses cardboard for everything.