The last ' is a closing quote mark, not a possessive apostrophe. "... will accrue to state elites" seems OK to me.
"... will accrue to state elites' hands" does not sound quite right to me. It's not usual for something to accrue to someone's hands. ("Fall into someone's hands", yes.) Your other two examples with "ours" and "son's" are, as you suspect, wrong.
Did you mean to highlight "China"? I can't quite see the significance of that in relation to your question. Apologies if I've misunderstood.