You should instruct the OOM Killer to not kill PostgreSQL. Memory is a global resource, even if you didn't overcommit the process getting the allocation failur

You should instruct the OOM Killer to not kill PostgreSQL. Memory is a global resource, even if you didn't overcommit the process getting the allocation failure is not guaranteed to be the misbehaving one, it's just the unlucky process that did the first allocation after all the memory was gone (this is also why handling allocation errors in your application is usually impossible, even without an overcommitting kernel).