Can my family do side-job in Japan by not employed？
If a foreigner with a family stay visa wants to work part-time, he / she can work by applying for permission to work outside the status of qualification.
Generally, it is said that permission is not required for one-off event support or sales of goods or services such as Mercari.
There are some side job options by not employed in Japan.
If you are teacher, there are some options as below
Since it is basically a Japanese-based service, you need to have reading comprehension and responsiveness in Japanese. The job of teaching in Japanese requires a high level of Japanese proficiency, but the job of teaching your mother language is ideal.
Street Academy- A market that connects what you want to teach and what you want to learn
ストアカ | 教えたいと学びたいをつなぐまなびのマーケット (street-academy.com)
Coconala -Japanese largest skill market -Buy and sell everyone's strengths
ココナラ - みんなの得意を売り買い スキルマーケット (coconala.com)
Time Ticketー Buy and sell personal time in 30 minute increments
タイムチケット | 個人の時間を30分単位で売り買い (timeticket.jp)
If you want to sell goods, there are some options below
Since it is basically a Japanese-based service, you need to have reading comprehension and responsiveness in Japanese. However, since it is a product sale, it is not necessary to have that level of Japanese ability to provide the service itself.
Mercari-Japanese giant goods Market on App
メルカリ スマホでかんたん フリマアプリ (mercari.com)
Rakuma-Japanese goods Market run by Rakuten
ラクマ（旧フリル） | 楽天のフリマアプリ - 中古/未使用品がお得！ (fril.jp)
Yahoo Auction- Japanese Auction run by Yahoo！
ヤフオク! - 日本最大級のネットオークション・フリマアプリ (yahoo.co.jp)
If you want to do simply hourly gig work, there are some options below
Since it is based on Japanese, reading comprehension and responsiveness in Japanese are required.
Lancers-Japanese largest crowd sourcing
ランサーズ | 日本最大級のクラウドソーシング仕事依頼サイト (lancers.jp)
Crowdworks－Japanese largest crowd sourcing