You mean, would I trust that a complete stranger was telling the truth when they said they wanted to get into the country because they feared for their lives and that they intended to follow the laws of the country and pay taxes etc.?
No, I wouldn't trust a complete stranger full stop, the circumstances of them being an illegal immigrant isn't suddenly going to change that. That's why it should be done through the legal process. Then their claims can be verified, they'll be registered and known about to the authorities so they're much more likely to pay taxes etc. and they should receive support and education to get themselves set up in the new country and possible learn the language.
No, that's not what I mean. Never said anything about a complete stranger, that was something you added.
Let's suppose that you know of a person who you are convinced is in danger and who you are convinced is going to be a law abiding citizen. For argument's sake we'll say that this is a person who was on a work visa, and while working in your country, there was a civil war in theirs, and currently a group they belong do (religion ethnicity w/e) is subject to harsh discrimination and possibly could be killed. You have known them over the course of their visa, and believe them to be a decent law abiding and honest person. They will not be able to follow the process needed to extend their visa or legally immigrate in time, and they do not have any legal recourse.
In this circumstance would you support their efforts to stay in the country illegally?