If you have a case pending with the Asylum Office and you move, you are supposed to file a change of address (form AR-11) within 10 days. It should be that easy, but of course, these days at the Asylum Office, nothing is easy.

The first problem is that if you move and you file a change of address, it could affect your eligibility for an Employment Authorization Document (“EAD”)–a work permit. Once your case is received by the Asylum Division, the “Asylum Clock” starts to count time. When the Clock reaches 180 days, you are eligible for an EAD (you can mail your EAD application after 150 days, but unless the Clock reaches 180 days, you will not receive the EAD). The problem is that if you do anything to cause a delay in your case, the Clock will stop and you won’t get your EAD, at least not for a long time. [Update 04/12/2017: Moving your case to a new Asylum Office should not stop the clock; this rule was changed by USCIS].
The Clock stops if you fail to appear for an interview or a fingerprint appointment, or if you move your case to a different Asylum Office–all these things are considered applicant-caused delay. Therefore, if you move, and the move results in your case transferring to a different Asylum Office, you may lose your opportunity to get an EAD (to see whether a particular move will cause your case to transfer to a new Asylum Office, you can check here).
In theory, the solution to this problem is easy: Don’t move until after you receive your EAD. In reality, it is not always so simple. People who file for asylum often do not have stable addresses in the United States (they’re refugees after all), and so it can be difficult to maintain a permanent address for long enough to receive the EAD. If at all possible, you should find a long-term address and use that address when you file your case. This will potentially save you a lot of trouble down the line.
For those unlucky few who must move their case to a different asylum office, you have to make a choice: Change your address–as the law requires–and likely lose the EAD (if less than 180 days have passed on the Clock), or violate the law by either keeping the old address (assuming you can still get mail there) or using another address within the jurisdiction of the original asylum office. If you choose to violate the law, you will probably get the EAD, but you could be subject to civil and criminal penalties (a fine and up to 30 days in jail), and it could affect the outcome of your asylum case (“So, Ms. Asylum-Seeker, you lied to us about your address. What else are you lying about?”).
Another problem for people who change Asylum Offices is that the transfer can cause delay (though I’ve seen examples both ways – usually a move makes the case slower, but in other cases, it seems to make the case faster). It may also put you far away from the lawyer who initially prepared your case or other people who are assisting you. There is not much you can do about these things, but they are good to think about before you file the case.
A third problem occurs when you move for a temporary period of time. I see this a lot: People move to a new city for school or work, but they do not change their “permanent” address. In this case, it is sometimes difficult to know whether to file a change of address form. If you change your address again and again, you will potentially bounce around between different asylum offices and never get an interview. On the other hand, the Asylum Officer might be suspicious if you list your home address in one city, but you are working or studying in a distant city. When my clients make a “temporary” move, I advise them to keep as much of their documents at their “permanent” address as possible: Driver’s license, tax documents, bank accounts, etc. Even so, it is unclear whether we are violating the law by not informing DHS about the temporary move. Indeed, the law itself (INA § 265) provides little guidance. At least in my experience, the Asylum Office is fairly lenient on people who make temporary moves, as long as there is evidence that they have maintained the permanent address.
As a lawyer, of course, I cannot advise anyone to violate the law by not filing a change of address form. But I would offer that if you are thinking about violating the law in order to get your EAD or keep your case from being transferred, you should talk to a lawyer first about your specific case. It may seem easy enough to not inform USCIS of an address change, but I have seen this play out at asylum interviews, and I recently almost had a big problem for one client who failed to inform USCIS about his change of address (let’s just say I was chastised by the Asylum Officer, which made me feel kind-of bad (Jewish guilt and all that), but fortunately, the client received asylum).
In the end, the best way to avoid a problem is to file the asylum application using an address where you can remain for a while. In the days before the backlog, when cases only took a few months, this was not difficult. But now, like everything else related to asylum, it ain’t easy.