Can she claim unemployment?...............
Doubt it. She was fired, not laid off.
She was formally hired, so no reason to believe she can’t.
Quinn Norton dated Aaron Swartz for three years.
Articles in The Atlantic and in New York Magazine indicate that she was pressured by prosecutors to offer information or testimony that could be used against Swartz, but that she denied having information that supported prosecutors’ claims of criminal intentions on Swartz’s part. Prosecutors nevertheless attempted to use a public blog post on Swartz’s blog that Norton mentioned, which may or may not have been co-authored by Swartz, as proof of a criminal intent.
SOURCE:
https://en.wikipedia.org/wiki/Quinn_Norton#Personal_life
Can she claim unemployment?...............
It depends on whether she has had enough other work in the past 15 months or so to qualify financially, and whether her separation from her most recent employer (NYT) was a firing for fault. She would probably get it because being let go during an initial trial period is not usually considered an at-fault separation. However, the NYT could claim that she was at fault because she hid information about herself, but they would probably lose. Most likely though, the NYT would not contest her getting benefits. The unemployment tax hit would be on her past employers she had during the 15 month base period, not the NYT.