Just to add on to what MUDLOGGER said, some sediment does subduct in a trench, in fact this is called an accretionary wedge. Don't think of it as chunks though, the aspect ratio on sedimentary rock is more like a piece of paper than a "block". i.e. wide and flat. So typically in continental crust collisions sediments, like sheaves of paper, just crumple and form the Himalyas or get skimmed off like California and glued to the side of a continent (think what it would look like if Japan got stuck onto the side of Asia). But when you have oceanic plate subducting under continental plate, some of the sediment can get pulled under the continental plate alongside the denser oceanic plate.

I wouldn't think of an accretionary wedge as a good place to form oil, too much stuff getting smashed up and moving around. Although, just a cursory glance at google showed me this which seems to indicate that there is at least the possibility of oil deposits in them.