I think that DHS and ICE should consider offering illegal immigrants who are first time deportees $5,000 for turning themselves in. According to current estimates it will cost $60 billion per 1 million deportations. If we were to pay the illegal immigrants to leave and have them sign concessions such as not being allowed back in for 7 years, then we could spend $5 billion per 1 million deportations. I assume with processing costs and other expenses it would likely be around $10 billion per 1 million deportations, but even at that number we will save over a trillion dollars over the scope of the entire deportation project.
The choices are simple, be forced to leave and receive nothing, or leave as a family with a bunch of cash to go back where you came from. People who are forcefully explled should be treated harshly if they ever come back, people who turn themselves in should have agrace period where they must leave the country before being allowed to come back through a valid port of entry.