Thanks Eirikur; I gave it a look but eventually found a more particular solution to this issue I was experiencing—which I have documented below.

Long story short, it appears that the issue was in the configuration of the flat file connection manager. After a manual review of the source CSV file I found stray double quotes that were not being used as qualifiers and were not escaped. I decided to revert the text qualifier field on the connection manager to <none> which did allow the package to complete execution, though it appears I have some text cleanup to do. I still don't understand why an error was never thrown during execution as is typically done when a CSV can not be properly read, but if anyone else ever runs into this, perhaps this might prove helpful.