In academia, "deadwood" refers to a tenured professor who produces nothing, earns no grants, and teaches poorly; it denotes a person who consumes time and money and resources without contributing anything of value. I am unfortunate enough to know a professor like this: her research stinks, she never publishes anything, her lectures are rife with out-of-date and inaccurate material, and (to top it all off) she's a tyrannical egomaniac. Unfortunately, she conned someone into giving her tenure, so her department is stuck with her.

Although it's virtually impossible to fire a tenured professor, deans and department heads often try to "prune the deadwood" by lowering the person's salary (or refusing to raise it), repeatedly moving the person's lab or office, assigning the person to lots of menial administrative duties, and in general making the person's life uncomfortable enough that they want to leave. Of course, such people rarely get offers from other places, so they remain more often than not.