closing a business

The lease obligation continues, despite the fact that the business went under, but the question of whether you are personally liable on the lease depends on the form of the business.  If, for example, it is a corporation, and the corporation is the lessee, then the individual shareholders are not liable on the lease (unless they have personally guarantieed it).  If the business is a sole proprietorship, or general partnership, the owners are personally liable for its obligations, including the lease.  Even where the corporation is a lessee, most landlords will insist on personal guarantees from its owners, unless it is a well established business.