The below looks at gearing a “Defaulting Investor” clause in a PE Side Letter in an LP’s favour i.e. in favour of the investor rather than the PE House.
Note, I have not recreated copied n pasted the clause as it would appear in the side letter, but rather I have broken the clause down into the various concepts that make up the clause. In doing so I hope a) to give an insight into the basic purpose of the clause and b) avoid infringing anyone’s IP rights.
LP Friendly Version
  (The LP, when demanded by the GP, fails to pay the capital it owes/originally committed to the Fund) (Such failure is the fault of the LP to a) make a capital payment or b) return distributions) (such failure includes the failure of any investor in the LP to make its contributions to the LP) (=the LP is defined as a “Defaulting Investor” at the point that the LP gives notice of its failure to the GP), (the LP’s rights in the Partnership is segregated into “Defaulting Partner” “non-Defaulting Partner” in proportion to the amount of capital not paid when called e.g. if the LP only makes 70% of its required Capital Contribution, then 30% of its interest in the Fund is treated as a “Defaulting Partner” ). 
 Note there is no overt restriction of the LP’s right to invest in other/competing investment funds.
 As a practical measure a GP friendly version of this clause would restrict investments into investment funds other than short term money market funds.
 An extremely pro-GP version would treat the LP as a Defaulting Investor, subject to the GP’s discretion, in relation to the entire value of the called for contribution. Though in practice especially in the current market, a clause would almost never be so “pro-GP.”
 A pro-GP variation of this clause would explicitly not that nothing in this clause, or the GP’s actions in relation to this clause would compromise the GP’s rights under the LPA to take action against the LP with regards to the interest allocated as “Defaulting Partner.”