Good question.
Here's an article I found:
http://www.nolo.com/legal-encyclopedia/bankrupt-tenants-how-new-bankruptcy-29689.html
"It's not uncommon for tenants with significant financial burdens to declare bankruptcy. The Bankruptcy Abuse Prevention and Consumer Protection Act of 2005, which took effect on October 16, 2005, makes it easier for landlords to evict bankrupt tenants. The steps you'll need to take depend on whether the tenant files for bankruptcy before or after you get a judgment against the tenant awarding you possession of the rental.
Tenant Files for Bankruptcy After You've Won Possession
If you sued the tenant for eviction and won a judgment for possession before the tenant filed for bankruptcy, you can proceed to evict the tenant, even if the tenant then files for bankruptcy in an attempt to stop the eviction.
New bankruptcy law vs. prior law. Under prior law, tenants could stave-off eviction by invoking bankruptcy's "automatic stay" with a last-minute bankruptcy filing. Under the new bankruptcy law, in this situation landlords can usually proceed with the eviction without having to ask a judge to lift the automatic stay.
Exception in some states. In a few states, and only in evictions based on nonpayment of rent, and in very narrow circumstances, a tenant can stop an eviction at the last minute by filing for bankruptcy -- if the tenant files a certification and pays back rent and forward rent. As the landlord, if you file an objection to the tenant's certification right away, you'll get a hearing in the bankruptcy court. If you convince the judge that the tenant's certification is not true, the court will lift the stay and you can proceed to evict the tenant.
Tenant Files for Bankruptcy Before You Win Possession
If you have not won a judgment for eviction when your tenant files for bankruptcy, and the tenant is (or becomes) behind in the rent, or violates another term of the tenancy (such as keeping a pet in violation of a no-pets clause), you can't deliver a termination notice, let alone start the eviction process. This prohibition is known as the "automatic stay."
Hearing to remove automatic stay. You'll need to go to the federal bankruptcy court and ask the judge to "lift," or remove, the automatic stay before you can evict the tenant. In most cases, you'll get the stay lifted within a matter of days and then you can proceed with your termination and eviction.
Exception for drugs or damage to property. You may find yourself needing to evict a tenant who is using illegal drugs on the property or endangering your property. Even if the tenant files for bankruptcy before you win a judgment for possession, you can still proceed with an eviction without asking the bankruptcy judge to lift the automatic stay. You'll need to prepare a certification that the tenant has endangered the property or used illegal drugs on the property (or had guests who used the property in such a way) and file it with the bankruptcy court (and serve the tenant with the notice). If your tenant does not file an objection within 15 days of being served, you can proceed with the eviction without asking the court to lift the stay. If a tenant objects, the bankruptcy court will hold a hearing.
Tenant Is Not Behind On Rent or Violating Lease
Filing for bankruptcy can affect a tenancy even if the tenant is not behind in the rent or otherwise in violation of the lease. After a tenant files for bankruptcy, the "bankruptcy trustee" (the person appointed by the bankruptcy court to oversee the case) must decide whether to carry on with or terminate the lease or rental agreement. In most situations, the trustee will let the tenant keep the lease, since it wouldn't benefit the tenant's creditors to force the tenant to incur the expense of finding a new home. However, if the tenant is paying an outlandish rent and there are plenty of modest rentals available, the bankruptcy trustee may terminate the lease and require the tenant to find a new home.
You do have the right to ask the bankruptcy court to demand that the tenant show proof of his ability to pay future rent, even if the tenant has never been late with the rent. If the tenant later becomes unable to pay the rent, you can ask the bankruptcy court to lift the automatic stay so that you can terminate the lease and, if necessary, evict the tenant.
For More Information
For more information on terminating a lease or evicting a tenant who has filed for bankruptcy, see Every Landlord's Legal Guide, by Marcia Stewart, Ralph Warner, and Janet Portman (Nolo)."