I once had a chicken who ripped her comb half off. It was a single comb, not a rose comb, but I just left it along and made sure no-one picked on her and left it alone. It did not get infected, but the ripped half ultimately turned black and fell off, and for the rest of her life she only had the front half of a comb.
(I know that mine ripped hers on hardware cloth, because she was broody and in a cage with on other chickens. She paced frantically, trying to get back to her nest, and at some point she had a ripped & bleeding comb.)
So if your hen's comb does not stick back together, there is a chance the back part may die and fall off. As long as it doesn't get infected, that should not be a big problem, but I'm mentioning it so you won't be as surprised if it does.
I notice someone already mentioned that you could cut off the loose part, which is also an option.