A corrupt, rural sheriff is pressured by his drug-lord bosses to protect their enterprise from the FBI while helping the feds search for an abducted girl.

I can sense an interesting story and tension hidden in this logline. You need to reshuffle and restructure this logline at least 10 times and believe me it will be quite fun to the possibilities.
My suggestion would be to put your protagonist in a position where he has to choose between his duty/ values and the dirty business he is in.

Example: A corrupt rural sheriff's life comes under jeopardy when he has to decide between his duty and the dirty business of protecting his drug lord.

Valentin's remarks in ver. 2.0 of your logline echo my major concern with the character.

As to the nuts and bolts of this version: while you do have a protagonist, he's introduced as "...being pressured by his drug-lord bosses" -- he's acted upon rather than acting. It's always better to describe the action with an active verb rather than a passive one.

And "protect their enterprise" -- is the drug-lord's goal, not the goal of the protagonist. "Helping the FBI" is not his objective goal, either; it's his job, what the FBI expects of him as part of their efforts to achieve their goal.

So I see this logline as describing a situation, an inciting predicament: he's caught in the cross-fire of the competing objective goals of others. That's good. But I don't see what his objective goal is in response to their objective goals.

Stakes: obviously, the life of the abducted woman is at risk. And he's in jeopardy of being killed by one party or incarcerated by the other. Again, this is good for the purposes of a dramatic dilemma: he's damned if he does and he's damned if he doesn't. But as Valentin suggested, his personal stakes ought to entail more than just saving his own corrupt derriere. His personal stakes should entail a moral, a thematic issue as well.

Like, the plot is his day of reckoning for the Faustian bargain he made with the local devils, the drug-lords.

Of course, you can't that cram all into a logline, but I hope it's in the story.

fwiw

Hey, dpg. Thank you for replying. I really do appreciate it, and I appreciate what you are saying. I feel like, however, that you are commenting on story elements when all I'm trying to do is write a logline. Granted, the above logline sucks. I rewrote it and posted it again. According to my understanding, a logline should be concise and present four essential elements: the protagonist, the goal, the antagonist, and the stakes. I think my new logline does that, but I may be wrong. I would love to hear your thoughts on the new one. I'm not sure a logline should necessarily contain the characters arc. I have no intention of having my protag be the same man at the end of the story, but the HOW that occurs should be left to the script and not the logline. Am I off base here? You tell me. Thank you again.