Traditionally, anyone arrested, at the local, or Federal, level, would have an expectation of legal due process.

Sure - but if they're here illegally, and they get turned over to the feds upon being arrested, then they'll face deportation on arrest. Getting due process for the crime they were arrested on (which, again, more likely than not results in no charges or acquittal) doesn't spare them from that consequence.

So people get reluctant to call in the police as often, because if they call the cops it might result in a person who is innocent of any present wrongdoing getting deported. Which is a pretty harsh consequence, so unless what's going on is really serious, a person who was considering calling the cops might think twice.

Ideally, someone properly convicted and imprisoned, would be deported to their home country, and handed over to the authorities there. Then the authorities in that country could decide to have him serve out his sentence in their prison, or walk free, on their streets.

I'm no international lawyer, but I don't think criminal justice systems work that way. There's treaties on international enforcement of civil judgements and other legal matters, but I don't think countries will keep someone in their own prisons based on a conviction from another jurisdiction without the prisoner's consent.

Plus - that's not without its own concerns. Do we want to leave it up to a foreign government whether someone who's been convicted here of a serious crime to perhaps just let them go free?