Means the opposite of "broad shouldered" (to act strong and confident and carry alot of burden/responsility in your stride). People (usually a manager) acquire this title by dodging work and/or making decisions and generally pass the buck onto a subordinate. This is done to avoid blame or to avoid doing a task that may be boring.

Somebody with slopey shoulders is somebody who deflects responsibility or tasks.

It's a step beyond lazy where the person accused is actively trying to push work onto somebody else.