Generally-speaking, it is a standard practice in Japan that his/her family member/family members take responsibility for matters when the person concerned cannot do something on his/her own.
ご質問ありがとうございます。
"Generally-speaking"＝「一般的に言うと」
"it is a standard practice in Japan"＝「日本では一般的なルールです」
"that his/her family member/family members take responsibility for matters when the person concerned cannot do something on his/her own."＝「本人が出来ないことに関して家族が責任を取るということが。」
ご参考に！
"In Japan, if a person can't take responsibility, then their family will instead."
"In Japan, if a person can't take responsibility, then their family will instead."
"In Japan" 「日本には」
"if a person can't ~" 「本人は〜できない場合」
"take responsibility" 「責任を取る」
"then their family will" 「代わりに家族がする」
アメリカ合衆国 
オーストラリア 
