so, what is my proposal for dealing with illegal immigration?

1) try them for it.
2) send them to jail for a few months for breaking the law. these should not be lengthy sentences, and in most cases will reduce to time already served.
3) give them a criminal record for entering the country illegally.
4) release them, without deporting them.

they will leave on their own relatively quickly, when they realize they can't get jobs with a criminal record. and, this should incentivize refugees to go through the process properly.