The show never really explains how Sunset is able to live without an income and more importantly... without documents that certificate that she should exist in the first place.
We get some small hints now and then. For example, the musical short video "Good Vibes" seems to point at a part-time job at a sushi restaurant (funny enough, I think someone made a fan art of "sushi Shimmer" before that episode was even made) but there is not much more to be said. Another episodes show her recording gameplay videos on some sort of Twitch/Youtube clone, but again we don't know is she can actually make an income as a video maker. What we have in the show really doesn't provide any direct answer.
What is really interesting though is that according to a recent twitter post of someone who worked on the show, the original Equestria Girls plot included a key event that was cut off.
My Little Pony: Equestria Girls
Season 2 Finale Thoughts
Nick Confalone - 10/15/17
The Mane 7 have come to expect that Equestrian magic will find them wherever they go from school halls to camp bonfires, cruise ships to amusement parks. Their friendship seems to be the sweet, lavender-infused honey that attracts the gnarliest of nefarious flies, buzzing with other-worldly enchantments. Like most heroes with geode superpowers, the girls have accepted their roles as always friends and often heroes, but the question remains: why does this keep happening? Many shows ignore this question completely to the detriment of their storytelling universe's reality-think: Murder She Wrote's Jessica Fletcher discovering hundreds of dead bodies, literally a new one everywhere she goes—but we're going to address this question head-on... because the answer is an essential piece of Sunset Shimmer's ongoing redemption arc, harkening back to the genesis of the Equestria Girls franchise.
Ever since Sunset's turn at the end of that first movie, her friends have reassured her that her past
is in the past—what matters is the good she chooses to do in the PRESENT.
...But they're wrong.
Unbeknownst to Sunset Shimmer, the powerful ancient-Equestrian magic spell she cast to open the portal to another world in the first place created an imbalance that has not been resolved. Her arrival in the human world displaced an innocent character whom we've never yet seen, but whose absence can be felt every time Sunset appears on-screen. In this final special of season 2, we're going to reveal what happened to the human Sunset Shimmer.
(source and archived images for reference in case the Tweet is removed: source, 1, 2)
As you can see in this cut script Sunset had an human counterpart. Without knowing the full detail we can't really say much, but it is indeed possible that the side-effect of this switching did explain in some way or the other how she managed to "get away with it" so far. Sadly, the author of the post didn't include any other detail, so I fear all we can do is to guess.
Maybe she just goes to Equestria, takes a few gems (those are so common there that the ponies use them to decorate cupcakes....) and then resell those at home.