I think the situation of stray dogs is sad, but at the same time I think they´re part of the culture for chileans, so the approach is very different for locals than for "gringos". I´m talking as a local here.
"Quiltros" (stray dogs and the word for mutts as well) have been around since always, people are use to deal with them, to feed them, and to pet them when they are nice and approach asking for a little love. There are some people that "adopt" some of these dogs, when they "live" close to their workplace o their homes, so they feed them in a daily basis, and sometimes take them to the doctor if they´re sick, even though the dog doesn´t live with them and technically they´re not the owners. I know that is not the ideal situation, and people and authorities should be more responsible, but again, that is the reality.
Here I´m talking in general, because in some places they build packs and turn dangerous, but that is not very common in an urban context. In the North they have big issues with that, and I don´t know why, over there quiltros are huge!
So, even when it looks like nobody cares about these guys, the truth is that a lot of people feed them, and keep an eye if someone is in a bad shape. I know tons of people that at some point has rescued a sick dog from the street, cure them, and wait till they find a permanent home for the dog, so that is a little "relieving" about the condition of the street dogs, and it shows how this interaction works socially.
I would love these guys to be neutered, but I don´t think it is a priority for authorities. I hope it can happen at some point. And the idea of killing thousand of dogs I think is just terrible. They did something like that some years ago around La Moneda before an official ceremony, and it was a big scandal, and believe it or not, the Carabineros hid one of these dogs in one of their cars to save him! So, forget it, people care in their way about quiltros, so killing them can´t be a public policy.
Right now an organization is opening a new refuge for cats and dogs that are in a bad shape. I think that is a nice initiative. They are looking for 130 people that can donate thousand pesos per month to pay the rent of this place (or less people that give more than mil pesos), so if you´re interested in helping with a little money, just PM me and I´ll give you the information.