I only have an example from the IT world. I fail to come up with a similar real-life situation where I'd be unable to decide which article to use.
Let's say I need to add a field (think column) to a table of a database. I might say:
I've got to add a status field to the users table.
Or as might be written in a log:
Added a status field to the users table.
If by "status field" I mean a field that contains some sort of status information, that would probably be okay. But what if "status" is a name (proper noun). That is, I want to add a field, that has a specific name, and most likely a specific set of values, to a specific table.
On one hand this field will be unique (not one of a kind), which suggests to use "the." But it sounds awkward (to me) to use "the" with an entity that doesn't yet exist, and hasn't been mentioned before. I lean towards the indefinite article. But what bugs me is that I'm talking about a unique thing.
What should I choose the first time I mention it? After that the definite article is probably to be used.