How does "Limited Liability" of LLP work?

Owners of corporations (private or public) are liable only to stocks they own. Creditors can't claim company debt from personal assets of owners because there's stock to distinguish from personal assets.

But, in LLPs, there's no concept of stock. How does personal assets kept separate here?

Note: I am not talking about shielding from other partners feature of limited liability.

You didn't state where you are, so I'm answering assuming you're in the US.

In LLP there's a concept of "basis". A partner is liable up to the basis of his partnership. This is similar to stock equity, except that there're no stocks. The basis is recalculated all the time based on the partner's share of income, expenses, withdrawals, contributions, etc.

It is basically very similar to LLC, except that in some jurisdictions professional services cannot be provided under LLC organization.

Here's a nice comparison of LLC and LLP.

The idea here is to separate the liability of owners from that of the company. When a company provides "limited liability protection," it means that the owners can only lose what they've invested in the company. That's true regardless of whether it's a stock-issuing corporation or a company that only has membership (or partnership) interests.

With a corporation, they don't actually lose the stock -- it just becomes worthless.

Note that it's always possible for the owner to AGREE to be liable for more of the company's debt. That might happen if, for example, he guarantees a debt. Also note that there are rare circumstances where courts ignore the limited liability shield.