Well it depends upon the situation its case to case basis

It varies. The Immigration and Nationality Act allows ICE to detain certain persons indefinitely while a judge determines whether the person should be allowed to remain in the U.S. Most persons are entitled to a hearing in front of an immigration judge, unless they were previously ordered deported. Some persons are eligible for release on bond, and can request a bond hearing from an immigration judge. Others are subject to mandatory detention and can only request release on supervision by ICE. In this situation, a week is usually sufficient for ICE to prepare and file paperwork with the immigration court. I would contact the local ICE detention and removal officer with authority over the file and find out what is happening. If it delays much longer, the detainee could complain or bring an action in court seeking relief from the delay.

It depends on the situation, but I read that if an illegal immigrant has been picked up by I.C.E. in most cases they have the right to appear for a court hearing. They can file an application for Stay of Deportation or Removal. If they have been detained for 90 days they should receive a Habeas Corpus.