First of all, keep in mind I am not a legal expert on landlord/tenant law. You may have to consult with an experienced attorney if your landlord decides to take “constructive eviction” action such as changing the locks, turning off utilities or leaving the property unsecured. Proper eviction is a lengthy legal process, not generally an immediate “get your property out of my apartment building by the end of the month or I’ll throw it all away” situation. You’re breaking the terms of a lease, and a landlord does have certain rights when it comes to finding new tenants and recovering as much lost revenue as he or she can.
You may want to check your original lease to see if there are any exceptions that would allow you to break the lease early. Some leases specifically allow tenants to break the lease if they become employed a certain distance from the property, often 50 miles or more. In your case, you have little choice but to appear at an immigration facility located out of the country. If the landlord does take you to court over the unpaid rent or the breaking of a lease, you or a legal representative could present your immigration situation as evidence and the judge may decide the landlord cannot legally evict you based on circumstances beyond your control.
Of course, there is also the possibility that the judge may find in favor of the landlord based on a strict interpretation of the lease agreement, but the solution may be financial, not a forced and immediate eviction. Generally, tenants have three months or so from the beginning of the eviction process to mount a defense for court or pack up their belongings and vacate the premises voluntarily.