If an illegal immigrant has been placed in jail, can an ice hold be taken off and how?

An ICE hold cannot be taken off unless ICE agrees to withdraw the hold, which they never do. However, there are certain procedure which ICE must follow with regards to actually taking the person into custody.

Your friend needs to speak with an immigration attorney as soon as possible. After he posted a bail with the criminal court, ICE can move him to another detention facility any time, without any warning. From New York state jails, the next stop is usually York, PA, and then one of the immigration jails in Texas, New Mexico, or, less often, Louisiana. If your friend had consulted an immigration attorney before, he would know not to waste money on the criminal court's bond - because he had no chance of being set free, and by posting the bail, he actually made his position worse (as I said, now ICE can ship him out of the state). If there is any basis in the law to prevent your friend's removal, it must be brought to the Immigration Court without any delay - before ICE ships him down South, where it will be much more difficult to bring witnesses and maintain the defense. If there is no way to get your friend permission to stay in the U.S., perhaps, he can get voluntary departure so he would not have a deportation on his record and might have a chance to come back legally one day; in some cases, it can be possible to bail the person out of ICE custody for the 1-2 months the judge would give him to get ready to leave the U.S. The bottom line is simple: get your friend an immigration attorney, as fast as you can.

Your friend needs to consult with an experienced immigration attorney as soon as possible. An ICE detainer under the circumstances you have described is unlikely to be removed. Depending on the facts, once he can demon state that his state criminal charges have been resolved, it is possible for your friend to seek a bond redetermination before an immigration judge whether DHS charges him into removal proceedings or not.