Are domestic pets the only animals which cannot survive without the assistance of humans?
I believe you are under-estimating "domestic pets"!
Have you never heard of "feral cats" and packs of " wild dogs" and so on!
If humans went extinct not all would survive for sure , but out of the many millions of cats and dogs that aren't chained up or locked in houses ....
lots would survive, cats on birds and mice etc and dogs on anything they could scavenge -and there would be a lot of that!!
Of the millions of domesticated horses and goats etc in paddocks and on farms -millions would suvive -all they need is grass and water after all!
So don't get carried away with domesticated pets not surviving without humans!