To my knowledge she wasn't threatened to get dropped but she did have competition on Def Jam. At that time Amerie and Terria Mari made their debuts too. Although they were marketed differently (they were R&B acts) Def Jam didn't have enough money to keep all 3.
Ultimately Rihanna was kept because unlike the other girls she had crossover appeal. She was more profitable.
- A similar situation happened with Christina Milan where she was let go because the label was spending money on Rihanna and not her.
I also think her relationship w Jay played a part in her being kept. Aside from Kanye, Rih is the only artist he has ever signed that he seems to really connect with.
She was going to be dropped the only difference is that her management were able to find endorsement to fund her albums. That's the only reason they kept her.