Is there a reason that she doesn't seem to voice the "a" at the end?
No, there's no reason. Probably the audio was incorrectly cropped.
It is there, but it is very quiet.
I can hear it only if I repeat it over and over ;-)
Great question, I came to the comments to see what others thought of the a at the end and the speaker not vocalizing it. I thought, o no, a new rule to learn!!!
She "swallows" the end of every sentence she speaks.
Could it be "This person"?
Not really. We'd say «ця людина» for 'this person', not just «людина».