At the moment, local police rarely do anything about illegal aliens except put them in US jails, at US expense. They are overwhelmed with their normal workload, and have neither the incentive nor the funds to help send illegal aliens home or turn them over to the Fed's to do so.
By contrast, local police are almost always very effective in locating military deserters and sending them back to the Armed Forces. Why? Since the Revolution, the federal government has paid a bounty, a generous bounty, immediately upon a local law enforcement agency placing a deserter in federal custody.
Why not do the same for illegal aliens? Local police forces could be granted a bounty for each illegal alien they turn over to federal authorities or place on planes back to their legal homeland. In addition, the police officer who recognizes that an individual is an illegal alien and starts processing his repatriation, should be a guaranteed a share of that bounty.
You can pay 50 bounties for the cost of keeping one illegal alien in a US prison for a year. Why not pay for the bounties with the federal funds now used to subsidize the states for keeping illegal aliens in American prisons? It would help solve the problem, improve conditions in US prisons and save money.