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.

What I see so far is a situation. A situation with dramatic possibilities. But what I don't see yet is a plot, his objective goal in response to the situation, his plan to survive both threats.

And no, he doesn't have to emerge a redeemed character. But there has to be a character arc: he can't be the same guy at the end of the film that he was at the beginning. He's got to become more than just another corrupt cop.

The movie "A Prophet" is the story about a young Arab man who is sent into a French prison for some petty juvenile crimes; he's no saint, but he has no intention of becoming a professional criminal. However the plot conspires otherwise; to merely survive, he must become a shrewd, hardened criminal.

Well, stories about young men who go into prison as innocent victims or at most petty criminals and emerge as hardened criminals are a dime a dozen. The character in "A Prophet" emerges as more than a hardened criminal; he comes out a mafia kingpin. That's the hook. Not just the situation, but the character arc, HOW he doesn't just endure but uses his wits to prevail, reverse his fortunes and reverse his relationship to the mafia boss he must work for, HOW the servant becomes the master. The character transformation is what makes "A Prophet" rise above its genre; imho, it's as compelling as Michael Corleone's in "The Godfather". And Michael's character arc is what makes "The Godfather" more than just another gangster film.

Just saying.

Are you suggesting that we should only write about nice guys or that I need to add an element to my logline to show his compassionate side (e.g., he has a son in a permanent vegetative state and he would do anything to get him the best care -- even take bribes)?

Yes he does deserve to suffer and he does. This ain't a Disney movie.

Regarding the DEA and FBI. Yes the DEA does deal with drug cases, but certainly if the FBI comes across drug trafficking in the course of an investigation they are most certainly going to refer it to the DEA.

Why should I care about a corrupt sheriff, sympathize with his predicament? Whether he gets legal justice from the Feds or street-justice from the drug lords, doesn't he deserve to suffer, to pay for being corrupt?

(And isn't the primary nemesis of the drug lords in the U.S. the DEA rather than the FBI?)