Poor (actual) sheep. They really get a bad rap in the world of human insults. Think about it: when you call someone a "lamb," that's a compliment—they're sweet. But when you call someone a sheep, you're insulting their intelligence, their willpower, and their ability to think for themselves. (Unless you're calling them a black sheep, in which case you're calling them a delinquent or a rebel without a cause. Sheep just can't win, guys.)
Someone should have clued Partridge in to how devastating the comparison to sheep can be:
"In addition to having the lower class of fused and broken wretches as servants, why not have a more or less handpicked population of like-minded sheep to herd into some new version of the planet that my father wanted to rule, solely? You were his sheep." (4.80)
Ouch. Although this insult is true—the Pures did follow Ellery mindlessly—it's still an incredibly alienating thing to say to a group of people that you're supposed to be leading. In fact, the truth hurts so much that more than a dozen Pures take their lives. Better to be mutton than sheep, we guess?
But the sheep-iness of Burn doesn't stop with Partridge's outburst. After he calls his constituency sheeple, Pressia sees an actual animal sheep in the woods:
The sheep has gray wool and a long twisted horn that curls over his skull. He's lost from his herd, maybe the only one still alive. (40.19)
Literature analysis tip: whenever you see the embodiment of an insult or compliment, it's a flashing neon symbol. Whenever a character has a meaningful interaction with an animal, it's also a flashing neon symbol. This little lost ram is a two-fer. Your symbolism alarm should be freaking out right now.
So what does this little guy symbolize? Unfortunately, at this point, he symbolizes Partridge himself. Partridge has gone from trying to lead to being led—he's the same kind of sheep he accused the Pures of being. Except, of course, he's a sadder sheep… because he's alienated himself big time from the rest of the Dome.
The sheep in the woods? He's:
[…] beautiful, alone, starving [and Pressia] can't help him. (40.21)
Partridge? He's pretty much in the same boat.