You are indeed at risk that your neighbor will contact U.S. immigration authorities (specifically, Immigration and Customs Enforcement, or ICE). However, nothing will happen immediately or automatically.

First, there is the question of whether ICE will act on this tip. They do not have the resources to follow up on every tip they get. They might simply ignore it.

Or, ICE might take a closer look and choose to exercise what’s called “Prosecutorial Discretion.” This means that they examine your situation — your history of responsible work and family life in the U.S., and your family ties to U.S. citizens (namely your daughters) -- and hopefully decide not to initiate removal (deportation) proceedings against you. The idea is that they are supposed to direct government resources at people who have committed crimes or are otherwise negative forces in U.S. society. Even if they’ve already set these court proceedings in motion, they can close them on the basis of Prosecutorial Discretion.

If ICE does decide to attempt to remove you, ICE agents may arrest you and/or your wife. This agency’s history of making sure that children are cared for in such a situation is not great, so make sure your children know where to go and who to contact if you are not at home when expected. It might be wise to consult an immigration attorney in advance about your situation, so that you have already lined up someone who can start acting on your behalf and figure out where you are being held.

After an arrest, you will most likely be charged with being deportable, released on bond, and then told to appear in Immigration Court on a certain day. A document called the “Notice to Appear” or NTA will describe the charges against you (that you’re in the U.S. unlawfully, most likely) and give you a date for your first court appearance, called a “Master Calendar” hearing. If you have any defenses to deportation, you can then ask for a full court hearing at a later date (called a “Merits Hearing.”)

For a review of some of the possible defenses that you might be able to raise in order to allow you to stay in the U.S., see Nolo’s articles on “Immigration Court Defenses: Avoid Deportation.”