to be (animate); to be; to exist
to be ...-ing
to have ...-ed; to be ...-ed
to (have the audacity to) do
父はまだ会社に居る。
My father is still at the office.
子どもの頃はよく川で遊んで居った。
When I was a child, I often played by the river.
あの人ならさっきまでここに居ったんだけどな。
If you mean that person, they were here just a while ago.