Frida has never been interested in love or commitment, so when her family suggested marriage to a Landgraab to tie the influential families together, she decided relocation was in order. While she hated the falling out with her brother, Gunther, coming to Moonlight Falls with her uncle Samuel and his new bride Olivia seemed like the perfect fresh start. Things seemed great until Uncle Samuel’s love for magic jelly beans caused his early demise. Olivia’s heartbreak led to distraction, which in turn led to an electronic accident and fire, resulting in not just one ghost in the house, but three. Frida has adapted well though, and being a ghost suits her just fine!
In The Sims 3: Supernatural, Frida Goth is a playable ghost living in Moonlight Falls with Samuel Goth, Olivia Goth and her uncle's fortune-telling friend, Helen Hall. She moved in with Samuel after her family tried to force her to marry a Landgraab. She therefore had a falling out with her younger brother Gunther.
However, her uncle died when he was poisoned by his favorite candies. His youthful wife Olivia (who is even younger than Frida herself) was distraught, causing an electrical accident that set the house, and then Frida, on fire. However, being a ghost suits her rather well.
Frida's presence in Moonlight Falls might explain her absence from the Goths' graveyard in Pleasantview, many years later.
Also she shares the grumpy trait with her brother, nephew and sister-in-law and the bookworm trait with Lolita Goth.
Life leading up to The Sims 2
According to the Goth family tree in The Sims 2, Frida is the sister of Gunther Goth, father of Mortimer Goth. This would make Frida the aunt of Mortimer, and thus the great-aunt of Mortimer's two children, Cassandra and Alexander. Frida never had any children and never married. Frida and Prudence Crumplebottom are not buried in the Goth graveyard with the rest of their family. In Frida's case, this may be because she moved in with her uncle Samuel in Moonlight Falls, and died there.
She does not appear in The Sims, at least, not by name. While it is possible that she is buried in Mortimer's cemetery, she could also be buried in Gunther's. It's also possible that she is alive somewhere outside of the neighborhood, or even buried elsewhere via Moonlight Falls.
Her ghost in The Sims 2 shows that she died of old age, but in The Sims 3: Supernatural, her ghost shows that she died by fire. It is possible she was revived before The Sims 2 and then died of old age. Or perhaps, it was simply the fact that in The Sims 2 (or in any game), an elder couldn't have an adult sibling and vice versa when being created in Create a Sim (unless third party hacks are used) and therefore, Frida Goth was an elder in the family tree, being a sister to the already deceased elder Gunther Goth. Considering Gunther was an adult in The Sims 3, it would only be logical to recreate Frida as an adult (though it isn't clearly established if she is an older or a younger sister to Gunther. Her facial wrinkles in The Sims 3 might indicate that she is older by quite a few years).