Good question. First, a remark: this comment is my application of anarchist principles to the question of deportations. As a diverse movement that values open and frank disagreement, there will certainly be anarchists who disagree with some of what I have said. I do not and cannot speak for all anarchists.

Sorry just wanted to check: you don't support deportation under any circumstances?

Basically no. I am an anarcho-communist, so I literally do not support borders and states, and I literally do not support deportations. I do not necessarily oppose running someone out of town or making oppressors' lives harder for them when they do heinous things, but I nevertheless oppose the system of deportations and international borders as a carceral, hierarchical institution.

But what about someone who overstays a tourist visa and is then continuously committing violent crimes? After they've served their sentence, what should happen to them?

"Crime" as a category should be abolished with states and laws. I.e., anarchism is an alegal order. That does not mean I oppose community justice processes, and that does not mean that we should tolerate oppressors. Literally the opposite! But the exact shape of justice should be up to the justice process in the local community where the person committed the violent crime, ideally individually adapted to the needs of the victims and other local variables. Visas should not exist because the system of national borders should not exist. Furthermore, I do not necessarily oppose disassociation up to and including physically removing oppressors from communities. I oppose the systematic, legalistic, geographical, carceral way that nation-states enforce borders.

If you can't deport them, then should they get a resident permit? Citizenship? If they don't then they'll just be in the country without the required documentation to work and reside there legally and will likely return to crime to survive.

Resident permits and citizenship should be abolished. You should not need formal paperwork with a State to be allowed to work. If the community decides to trust the individual again then that's their business that they have to freely decide. Furthermore, if an oppressor does something really heinous enough, I do not oppose the existence of a system of agreements between communities that keeps track of people who commit certain specific violent acts. E.g. even though I am against states, I support a world where it would be practically impossible for someone like Jeffrey Epstein to ever get back his reputation. (Remark: the State was content to allow Epstein to walk the first time he was caught, and *insert the various intersectional oppressions perpetrated by capitalists world*; i.e., States are not immune to the failure mode of letting creeps off the hook. In my view, States exist specifically to let certain oppressors off the hook.)

[Criminals] will likely return to crime to survive.

The means of survival should be unconditionally guaranteed on the basis of being sentient. I.e., you should not have to work to survive. E.g., even the human traffickers get to eat, even if you kill them in defense against future oppression after they have shown themselves unwilling to stop doing human trafficking. (I understand that this is a counterintuitive position, but it is not a contradiction!) If a person then uses their gift of sentient life to oppress others, that oppression should be smashed and its effects reversed with a minimum of violence. Emphasis on minimum: the minimum might not be zero. It might even be a war (e.g., revolution against the capitalist class).

Not to mention how appealing a country with this policy would become for human traffickers.

Indeed. If a community itself becomes a haven for human trafficking, that community itself becomes an oppressor. Then, that new oppression ought to be smashed by all the free people in the world, in particular the neighbors of that community, even with violence if needed. States merely make this process more challenging to actually implement, in particular when the oppressor is connected.

there are surely better ways to protect migrants.

There surely are better ways to protect migrants, but simply abolishing deportations without abolishing the State and all other hierarchies, without taking any other measures to keep migrants safe? That's not really what I'm advocating. Ending deportations is merely one part of a much more comprehensive program of anarchist communism.

IMO this is a challenging question for anarchists to answer... because justice is inherently a challenging problem to solve. In my view, anarchists would have an easier time answering this question compared to statists because our worldview is easier to adapt to a changing world (unlike States, which impose the will of the capitalist class on the world), save for one simple fact: the statists' answers are treated as "gospel", and thus self-evident and therefore not needing justification, since they are already the dominant answers in global society. And they are the dominant answers not because they're particularly fit for purpose, but because of a long and complicated history of domination and imposition by various oppressor classes, i.e. by generations of state violence.

Just chiming in to say that deporting a problematic person just makes it someone else's problem so you're not really fixing anything in the end.