Peripheral pragmatic needs are often linked to as-yet unidentified or unclear future goals. Having a second language is undoubtedly good for future employment prospects, future travel, etc. Often, this quadrant goes hand in hand with one of the others, since most families are aware of the advantages bilingualism brings. It does become particularly important in families where there are opposing views, for example, where one parent has a strong emotional connection to the language, whereas the other can mainly see a generic, peripheral, pragmatic advantage to it. In such cases, it can be difficult to design and maintain a suitable family language policy (e.g. how the various languages are used in the family), due to different opinions on what is important. In such cases, it is particularly important to communicate within the family, explore the origins of differing attitudes, and seeking to resolve them.
In some families where multiple languages are spoken, one language may hold a strong emotional (or pragmatic) position, while another language falls more into the peripheral category (for example, one language may be of particular importance in the family, while another may be more widely spoken world-wide, leading to a peripheral/pragmatic attitude that it would be useful to maintain it). In such a conflict, it is unsurprising that the language linked to the peripheral/pragmatic is less likely to be used and maintained long-term.