For the purposes of full disclosure, a few points:
I am not a supporter of illegal immigration, on its face and in principle.
Nevertheless, the issues surrounding illegal immigration can be complicated, so it makes sense to assess people on an individual basis,
The advantages of illegal immigration in certain volumes may outweigh the disadvantages (eg for the purposes of food production).
One knock-on effect of illegal immigration is that it will put downwards pressure on wages for certain sorts of labour.
The US wall is unlikely to work as advertised. The mass of illegal immigration involves legal entry and overstaying a visa. But I understand the frustration of people who object to illegal immigration.
Illegal immigrants should be treated with respect. It seems likely that most of them are perfectly decent, otherwise law-abiding, people.
There are also refugees, for whom the expectations are different. There clearly is a difficulty distinguishing genuine refugees from people purporting to be. And some wrong decisions will be made in doing so. A fake refugee is a type of illegal immigrant.