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 generallypass 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!
The large protrusions that extend outward from Jeremy Lopez's chest. At the summit of the slopies like a giant nipple which weaps warm milk. Under the slopies lie centuries of built up grode that would be useful when fulfilling an order to genocide some people.