What is it called when the subject of a sentence is the same as the object of the previous sentence?
I'm going to Freddy's house. Freddy lives down the block. The block is paved with gravel. The gravel is jagged.
I'm not aware of a specific term that denotes the use of the object of the previous sentence as the subject of the next. But your sentences follow a common pattern in English syntax called Given-New. Speakers and writers typically start with information that is known to the recipient and follow it with new information.
There is a good introduction to this here: Given-New.