There is no statute of limitations for illegal immigration like there is for many crimes.
In Minnesota, for example, charges in most crimes have to be brought within three years, after which the perpetrator cannot be prosecuted. Arson is five years, as is theft, forgery or fraud. Bribery of a public official is six years. Sex offenses against adults are nine years. Kidnappings and death crimes have no statute of limitations. (Source)
Our current system has no statute of limitations for illegal immigration, which isn't even a crime in most circumstances. No matter how long you've been here, you never emerge from that threat of deportation. An illegal immigrant could get in more trouble for simply being here than for arson, theft, bribery, or sex offenses.