Do you open the door?
A common misunderstanding is that, simply because Immigration Officers are at your door, you have to let them in. This is not the case. First, stay calm. Second ask the officers to slide their warrant under the door or hold it up to the window so you can read it. If they do not have a warrant, you do not have to let them in. If the warrant is for searching the home, you have to let them in. Open the door and step aside. When the officers have a warrant or order for removal/deportation, however, you do not need to allow them into your home. If you choose to cooperate, you can simply step outside and close the door behind you.
Do you have to answer their questions?
The simple answer is, no. Remember that you have the right to remain silent. In fact, I routinely instruct clients to provide their name, say wish to remain silent, say they have a lawyer and give the officers one of my cards. Also, you have the right to an attorney, but the government is not required to provide one to you. So, do not feel like are obligated to answer their questions without legal advice or assistance, and do not let fear overcome the fact that you have rights which can and will protect you.
Should you sign their papers?
Again, the simple answer is, no. Not without first consulting with an attorney. When Immigration officers present you with documents agreeing to voluntary departure or some similar action, you are generally waiving more rights than you are aware of. And, you are losing out on the opportunity to try to fight to stay in the country. And, signing one of these documents, then failing to follow through creates even more problems for you. If you are asked to sign something, ask for time to review it with an attorney first. If, after reviewing the terms and the consequences with a lawyer, you think signing is the right decision, then so be it. But, at least you have not blindly forfeited any rights or opportunities.