The laws where a known criminal could not be held for deportation clearly need to be changed. But yes, the reality is that if you put every illegal immigrant in a state of constant fear of deportation all the issues with illegal immigration actually increase (more crime, economic impacts, people living in shadows, etc)

Some reading:

https://en.wikipedia.org/wiki/Alabama_HB_56
https://en.wikipedia.org/wiki/Arizona_SB_1070