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.
Officeworker 1: Dave the manager has just given me a pile of accounts to work on thats going to be externally audited!!
Officeworker 2: But he's more qualified than you to do it! Jeez that guy has got such slopey shoulders!
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.
He wants her to do his work for him? Old Slopey shoulders strikes again.