Is there any situation where it’s acceptable to not perform AML/KYC on Limited Partners during a fund closing process?

TL'DR - No. All Limited Partners must go through an AML/KYC prior to being accepted into the fund during an proper institutional grade LP onboarding process. This is because banks perform significant compliance checks on onboarded LPs. When a bank determines that an LP is not compliant, they typically shut down the bank account and often report this action to the regulatory authorities.