If the stuff on her butt smells, it could be vent gleet. You can search for that on here and see if it sounds the same. You'll also find info on how to treat it.
If the stuff on her butt has a yellow tint and looks like egg yolk, you might want to research egg yolk peritonitis. I lost a black sex link girl to it earlier this year she was about 3 1/2 years old. My first 4 hens were sex links and it seems to me that they have a predisposition to have reproduction problems, a shorter egg laying span, and a shorter life span than the heritage breeds. The first two years they lay like crazy but they decline quickly after that, at least mine did. Of the first 4 that I got not quite 4 years ago, I only have 1 left and she was never a good layer, hasn't laid an egg in over a year. That's probably the only reason she's still with us.