Except in very exceptional cases, shares in private portfolio companies contain restrictions on transfer and cannot be distributed to LP's.
Publicly Traded Shares
Publicly traded shares can often be distributed to LP's. Distributing publicly traded shares "in-kind" allows individual investors to make their own decision for when and how to sell their allocation of shares.
In-kind share distributions usually occur after a portfolio company goes public or receives public company securities as part of an acquisition.