From the gifs it doesn't really look like any of the champions are dead it looks more like they are asleep for the most part, In Zeds Gif there are flower petals blowing in the wind and In Sonas there are butterflies and a sort of mist, both of these seem to be symbolic of something I'm just not sure what. Butterflies are often associated with being representations of the soul, and since these ones are white and transparent I'd say that's probably what they were going for. The flower petals as far as I know have some "changing of the season" kind of meaning typically. Both the mist in the Sona video and the plants in the Zed one are coming from the champions themselves, so I'm guessing it has something to do with testing the spirit of the champion or something.
The gifs for Garen and Vi I'm less clear on, Garen seems to have his face shatering on the side around his right eye and a green glow, surrounded by emerald shards, and Vi has a pinkish glow emanating from her chest and small shards of something surrounding her, maybe dust.
Maybe the link is that each champion had something taken from them, Sona has no voice so her neck is cracked, Zed was consumed by shadows so he lost his reason or humanity and his mind is consumed by the plants, Vi lost her memories(in some grim event relating to her old gang) so she lost something she cared about, either literally through it being taken away or from not rememnbering it, so her heart is affected, Garen is "The might of Demacia", and is a high ranking soldier in the Damacian military, he has become a symbol to those around him and even though something(Katarina) might have affected some sort of change in him he is still expected to be the shining example that all of Demacia can work towards, so his face(or mask) is cracking. Sona Had her voice taken, Zed had his mind taken, Vi had her heart taken, and Garen had his will taken.
I'm guessing if this is a new champion they have something to do with being able to see someones soul or something to that effect, maybe being able to enter dreams.