Positive pregnancy test with tubes tied?

I’m actually asking for my sister. She got her tubes tied I think 2 years ago now. Back in July she was feeling off and took a pregnancy test that she had at work (she works at a hospital) and it was positive. She took another from a different brand and it was still positive. I made her take one 48 hours later and the line was pretty much gone and when she went to her doctor her HCG levels were almost back at negative. 3 days ago she sent me a picture of another test that was positive. It was super faint but still positive. She took one today and the line is definitely darker. What are the chances of this baby sticking? And has anyone gotten pregnant with their tubes tied?

This was 3 days ago

And this was from today