I would be rather curious about how your girlfriend would get deported if she can't enter without a visa.

There is a website Italian Foreign Ministry that allows applicants to determine whether or not they need a visa. And if you check for Chilean citizens living in Chile you will see that they need a visa.

So first things first. She will need to get Schengen visa from the Embassy in Santiago, which will likely require her to provide an itinerary and other relevant information and then everthing will get clarified.

I would be rather curious about how your girlfriend would get deported if she can't enter without a visa.

There is a website Italian Foreign Ministry that allows applicants to determine whether or not they need a visa. And if you check on the site it will show that she will need to provide the proof of duration of stay. Basically usually referred to proof of onward travel (return ticket)