袖の振り合わせも他生の縁
ふでのふりあわせもたしょうのえん
even accidentally touching sleeves with a passing stranger is caused by fate
ない袖は振れぬ is read as ないそではふれぬ (naisode ha furenu) and means you can't give (use) what you don't have.
ないそではふれぬ
naisode ha furenu
ふでのふりあわせもたしょうのえん
even accidentally touching sleeves with a passing stranger is caused by fate