The lease is not automatically rejected in most bankruptcies. However, if you do not stay current with your post filing lease obligations during bankruptcy, the landlord will move to reject immediately your lease and retake your possession. If a trustee is appointed, the trustee will oversee the liquidation of your inventory. Your bankruptcy counsel will be able to guide you through this process.
The answer to this question depends on a number of factors. First, who filed bankruptcy: an individual or a business entity such as a limited liability company or corporation? Also, is the tenant listed in the lease a business entity or is the lease in the name of the individual who filed bankruptcy ("debtor")? Is there a personal guarantee signed by the debtor? Second, was the lease assumed or rejected in the bankruptcy case? If the individual or business debtor filing the bankruptcy was a tenant on the lease, it is required to state their intention whether to retain the lease space or vacate the lease in their bankruptcy case.
I recommend you speak to a bankruptcy or real estate lawyer before speaking to your landlord about the timing of vacating the lease space. Best of luck.