How tiny can a queen be?

Well, I gave one hive to a neighbor, and then my remaining hive swarmed, leaving 6 empty queen cells and only a few bees. As in maybe 4 dozen workers. I figured the hive was toast

Today I took it apart, freezing the empty combs to kill any pests. I noticed they are now down to 2 dozen worker bees. But, what is this???? They are feeding what looks to be a tiny, skinny black bee. In fact it is build like a queen but it is only as long as a regular worker bee. It has no fuzz, and it is built like a queen, but, WOW!

I am not sure but I think that is the queen that was left after the hive swarmed. If so, the hive is still probably hopeless, as there are not enough bees to support a hive and it looks like an early Fall. And, she is not doing a very good job of keeping her bees from drifting off.