The case of a New York City grandma who's been missing for two weeks in Las Vegas took a sad turn Thursday ... and TMZ is learning more about what happened to the 63-year-old.

Alisa Goods was visiting a friend in Sin City, and she left their home on August 8 to go shopping at CVS and vanished. Days after she disappeared, someone began messaging from her phone, asking her family for bitcoin. She was found dead Thursday near Harry Reid International Airport.

Las Vegas Metro PD tells TMZ ... surveillance from the airport shows a woman, believed to be Goods, falling down an embankment -- getting back up and then collapsing on August 8.

As we previously reported ... it was the area surveillance that led authorities to her body ... but why she was there wandering around -- and who was using her phone afterward -- are total mysteries.

Police are playing this one close to the vest -- and won't comment on the cause or manner of death -- but her family ... along with everyone else following the case that's made national headlines, want answers.