Here is the passage again:
Ralph spent all his savings on a diamond ring to give to his girlfriend
Gloria. A greedy young woman who had a box full of expensive
trinkets from ex-boyfriends. Gloria was always looking for a man
with a fat wallet.
The second part is an appositive fragment. All you have here is a noun phrase renaming Gloria. This phrase does not have a main clause, the necessary component of all complete sentences.