Lab has confirmed on the OS vulnerability update for your request:
In Software ESM (or any s/w version of our products), the O/S is the responsibility of the customer.
They should thus upgrade it themselves, with the limitation that a given ESM version may have only been certified on a small set of RHEL versions.
For example, ESM 6.5 is likely not certified on RHEL 6.8 (latest 6.x version at this time)
They will be in an unsupported configuration when OS updates that upgrades the Kernel/Release version. That is the impact. The full extent of impacts will be unknown because we do not test that.
ESM 6.5.x latest (6.5cSP1/P2) does NOT support RHEL 6.8.
NO further platform support is being added to RHEL6.5, which has been announced End of Life Dec 2016.
To achieve RHEL6.8, there is not yet a certified version.
We expect (not confirmed) 6.8c Patch 4 and 6.9.1c Patch 2 will add support for the 6.8.x and 6.9.1.x codelines respectively. Neither is released yet.