"Perpetual Succession" in a company is best defined by this line -
Members may come and go but the company goes on forever.
It is one of the fundamentals of a company's existence. Perpetual succession means that a company's life is not determined by the longevity of its members, shareholders, promoters, directors, employees or anyone else. If a shareholder dies, or hypothetically, all the shareholders die, only their shares in the company will be transferred to new people. If even a key director resigns, he/she will be replaced but the company will continue on.
"Limited Liability" defines the obligation of the members towards the company. It is the maximum amount owed by shareholders to the company. For example, if a shareholder owns 1 share of $10, then under no circumstances, he can be made to pay more than that by the company. That is, his liability becomes "limited".