If the fund underperforms severely (e.g., fails to return even 1x capital), what LP exit options (if any) exist beyond secondary sales?

Generally speaking, there are no easy exit options for limited partners should a fund underperform - this is why it's critical for limited partners to carefully evaluate and perform due diligence on any fund managers they intend to have manage their money for a decade or more.  

In most cases, secondary sales are also not an easy exit option.