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.

Deffeyes addressed the question of finding oil in the ocean bed beyond the shelves in his '01 book. He describes the necessary conditions for formation of oil, then states:

So now we have an agenda:an oil province has to contain organic rich source rocks, and the source rocks have to have been buried below 7500 feet but no deeper than 15000 feet. If these ingredients are not present, no amount of drilling is going to find oil. Here's an example: the sediments on the floor of the deep sea are about 3000 feet thick. Even if organic rich layers were present near the base of the sediments, they would not even be half way to the top of the oil window. This paragraph wipes out 60% of the earth's surface as a potential source for oil.

It would have to be some new-fangled kind of oil to have formed there I guess.

There was drilling deeper than 15,000 feet that discovered oil in offshore sedimentary basins. Water was less than half the weight of rock and salt was lighter than most rock. Although oil was found deeper than 20,000 feet below surface it have formed before more sediment piled on top and the earth's crust became compressed and lowered with the extra weight burden. The deposition of delta sediments offshore created a huge wedge of sediments that caused a trough in the basement rock as the rock had some elasticity or plasticity. Over millions of years rock layers were folded or bent. These troughs were huge synclines.

As for further offshore in the middle of the sea, there was less sediment and more basaltic basement rock without the thicker accumulations of organic sediments found near shore. It is not likely one will find hydrocarbons beyond the continental shelf areas. The oceanic crust subducted under the coast of Oregon contained sedimentary rocks and as the subducted rock sank towards the mantle these rocks melted and formed various volcanic and intrusive lavas containing more felsic and silica rich melts than the oceanic crust that subducted with the leucocratic sediments.