这个句子不对!
你看中间是一个逗号 ,最后是一个句号.所以说明这一个长句子没有链接副词 或者连词
一下整个大句子是正确的：
His mother is ill,so he has to look after her at home.
His mother is ill and he has to look after her at home.
既然没有连接词 那么这句话是一句话 就是错误的!所以要写成独立主格的形式：
His mother being ill,he has to look after her at home.
= with his mother being ill,he has to look after her at home.=with His mother ill,he has to look after her at home.