In company law, perpetual succession is the continuation of a corporation

Corporation

A corporation is created under the laws of a state as a separate legal entity that has privileges and liabilities that are distinct from those of its members. There are many different forms of corporations, most of which are used to conduct business. Early corporations were established by charter...

's or other organization's existence despite the death, bankruptcy, insanity, change in membership or an exit from the business of any owner or member, or any transfer of stock

Stock

The capital stock of a business entity represents the original capital paid into or invested in the business by its founders. It serves as a security for the creditors of a business since it cannot be withdrawn to the detriment of the creditors...

,etc.

Perpetual succession, along with a common seal, is one of the features defining a corporation's legal existence as separate from those of its owners.