Whether that is the requirement?
Once a partner with equal share in profit and loss - how does it matter?
Further, if A has done some mischief, then B has to take appropriate legal action against him. Which she cannot do because the Partnership is not registered. If she is totally unaware of A's activities, then it is her irresponsibility and negligence.
If the Partnership is liable to much more than what is the capital, then yes, the partners are liable. AFTER ALL IT IS NOT A PRIVATE LIMITED COMPANY, where the liability is limited.