How Postgres Parses Conditional Expressions in PL/pgSQL

Deepak Mahto parses a command:

At first glance, this code block seems incomplete. Notice the IF condition: it appears to be missing an additional condition after the AND operator. Logically, this should cause an exception due to the incomplete condition following AND.

  IF i = 0 AND THEN 

However, during PL/pgSQL execution, the condition is evaluated without any syntax errors or warnings. This raises a critical question:

How does PostgreSQL internally process this condition?
What allows this seemingly incomplete expression to work?

Read on for those answers.