I simmered it all night, cooled it immediately in two small containers, and didn't end up needing all of it. May I still divide it into even smaller containers and freeze it safely?
Are you channeling your best self with this comment? (If you're not sure, check out our Code of Conduct.)
Six days is past the recommended (refrigerator) storage time. The USDA recommends that you discard it. If it were me, however, I'd bring the stock to a boil for 10 minutes then cool in an ice bath before freezing. There are those who will argue against doing so and I think that's fine tack, too. It's hard to go wrong following USDA recommendations.
Here is what Harold McGee has to say about the situation:
"a fine tack"
Freezing will suspend the stock's current microbial state which is probably fine but technically suspect at this point. Boiling will reset the clock so to speak.
Let's settle this once and for all, shall we?
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