"Assuming that the house is paid for, of course; if your net worth is really only $300K, odds are you don't have the house paid for either"
Person A has a paid off house. If their net worth is 300k that implies a low cost of living area, and a small house. They likely are used to living a modest life (most people when given more money will spend it on a better house). They won't need much money, and better yet, since their house is paid for, they don't have to pay rent with their income. Of course it is entirely possible they are "party animals" who never are home and only need a tiny house for an address, and they spent every penny they earn on alcohol for their 'friends' - but this seems unlikely.
Person B doesn't have their house paid off (living in an apartment counts!), and their net worth is 300k. The question then becomes how much are they paying for housing every month, since this reduces their spending ability.
Neither person will have a great life (assuming they live in the US - 300k net worth in a poor country is considerable wealth), but a paid off house allows for a nice life, while paying for the house means scrapping by.
I don't understand, is it paid for or not?