Basically, that is a domesticated animal, whose ancestors have lived and worked with humans for hundreds of generations. Animals who are no longer equipped to fully fend for themselves. Animals abandoned by the humans they depend on.
Can an abandoned cat survive? Perhaps yes.
Can abandoned cats mate and produce subsequent generations that have not known mankind? Yes.
But it's not a good deal for anybody. It's not good for the cats, who live shorter, poorer lives. And it's not good for humans, who often find stray or feral cats to be a nuisance.
If we get them young and friendly enough, they might find homes as indoor cats, members of the family.
If they aren't friendly enough to be adopted as indoor pets, there is still hope that they might become outdoor pets.
NOTE: Sometimes, in order to trap a cat, you have to feed it in a known location so that it knows that food is available there, and is more likely to go into the trap to get it.
We always use humane Havahart-brand traps. They do a good job of catching the critters without hurting them.
We don't want to kill them. Neither do we want them to continue the cycle of more kittens...