"Attrition through enforcement" or just "attrition" is a commonsense, demonstrated plan to reduce the numbers of illegal aliens in the U.S.
Under attrition, illegal aliens would be encouraged to "self-deport" - to voluntarily leave the U.S. - rather than having to be removed through immigration enforcement. Under the plan, we would decrease the job opportunities available to illegal aliens at the same time as reducing the non-emergency public services available to them. Once that is done, many illegal aliens will make the rational choice to leave voluntarily. Just as importantly, many fewer people will try to come to the U.S. illegally when they realize they won't be able to find work or access public services.
Attrition has worked in the past and continues to work to the extent that it's been tried. For instance, many illegal aliens have decided to leave U.S. states that have passed their own immigration enforcement laws, such as Georgia (link).
Consider the figures from Pew Hispanic (link) showing that the number of illegal aliens in the U.S. was 12 million in 2007 but fell to 11.1 million in 2009. Where did those 900,000 people go to? The answer is that they self-deported: most no doubt realized that due to the economic downturn in the U.S. it would be better for them to return home.
The problem is that attrition hasn't really been tried: it's so far been very difficult to reduce job opportunities available to illegal aliens or to reduce the services available to them on a nationwide or even state basis. Those who want to profit from illegal immigration push to give benefits to illegal aliens and to make it easier for them to find work in the U.S. See Obama immigration, Gil Cedillo, California, Rick Perry, Michael Bloomberg, Antonio Villaraigosa, DREAM Act, Mexican government, sanctuary cities, Center for American Progress and hundreds more pages here for examples of profiteers seeking to give benefits to illegal aliens or to make it easier for them to work in the U.S. Without the influence of those profiteers, many more illegal aliens - unable to find work or to access non-emergency services - would make the rational choice and decide to leave (perhaps even assisted with some form of repatriation program).
Some mock the concept of attrition and self-deportation, but they aren't in touch with reality: hundreds of thousands of illegal aliens over the past decades have decided to self-deport.
Some might doubt that attrition and self-deportation would work to greatly reduce the number of illegal aliens in the U.S., but that's because it hasn't been tried on a nationwide basis due to those profiteers mentioned above.
And, many illegal immigration supporters try to hide the entire concept of attrition and self-deportation from you, including president Obama, many other politicians, and the establishment media. For a longer discussion and examples of them trying to keep you in the dark, see deportations false choice. Even some of those who disagree with this site on attrition will (hopefully) support having a debate about it rather than trying to keep people from learning about it as discussed at the last link.