~는/은/ㄴ 편이다 = Tends to, Often. This Korean Intermediate grammar point is used to express a TENDENCY rather than making an assertive and clear statement of a fact. One often uses words like 많이 (Many, A lot), 자주 (Very, a lot) etc. with this grammar point. After action verbs we use 는 편이다 After Descriptive verbs we use 은(if verb ends in a noun)/ㄴ(If verb ends in a vowel) 편이다 ~ 는/은/ㄴ 편이다 Example: 친구들과 전화를 자주 하세요? (Do you often call your friends) 응, 일주일에 세 번쯤 하니까 친구들과 전화를 자주 하는 편이야. (Yes, I call my friends about 3 times a week, I tend to call my friends a lot) 영화를 많이 보세요? (Do you watch a lot of movies) 네, 일주일에 두 번쯤 보니까 자주 보는 편이에요. (Yes, I tend to watch a lot of movies, about two times a week) 저희 집은 잘 사는 편은 아니었어요. My family did not tend to live well. = My family was not really rich.

Actually there is a word for "rich". 잘살다 means to be well-off or well-to-do, essentially "rich". It is a separate word distinguished from 잘 살다 (dictionaries list it as such too), so your example sentence should have said 잘살다 instead of 잘 살다. 잘 살다 usually means "to live free of trouble", which can mean different specifics in different contexts. It usually doesn't mean being well-off. In speech, 잘 살다 is pronounced like two words, with 잘 made longer and emphasized. 잘살아 is said like an ordinary word. Here's an example. - 내 친구네는 잘살아 = My friend's family is rich/well-off. GOOD (Natural even as an isolated sentence) - 내 친구네는 잘 살아 = My friend's family is living well. ?? ("living well" seems vague and unclear, if there's no context)