Which system of social stratification was in the final stages of breaking down when karl marx developed his ideas?

The correct answer is feudalism.

Feudalism refers to a social stratification system from medieval Europe, where people worked for land owners (the powerful minority) and offered them protection in return for land and a place to live. A feudalistic society consists of the king (who's at the highest rank of the hierarchy), followed by nobles (priests and princes) and then peasants.