Life leading up to The Sims 3
In The Sims 3: Supernatural, the middle-aged, dearly-departed and spinster Frida Goth is a playable ghost living in Moonlight Falls with her uncel, Samuel Goth, his young wife Olivia Goth and her uncle's fortune-telling friend, Helen Hall. She moved in with Samuel after her family tried to force her into marrying a Landgraab, and consequently had a reluctant 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 on fire, and then Frida. However, being a ghost suits her rather well.
Her 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, the bookworm trait with Lolita Goth, and the perfectionist trait with her sister-in-law.
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. She never had any children and never married. She 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. Considering her spectral existence and a lack of attempt to make things up with her brother Gunther, it is very much unlikely that she would be somewhere outside of Moonlight Falls.
Her facial structure is near identical to that of the 12th face template in Create a Sim, except the slightly customized jaw. But the difference is so small that it can only be proven through BodyShop. Her face is almost identical to that of Francisca Pantalone and Denise Jacquet.
Considering her brother 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.
Although she is not resurrectable in-game, She can be brought back via Tombstone of Life and Death, or by relinking her character file in SimPE. This is the case of all deceased members of the Goth family.
Strangely, when viewing her information in SimPE, it can be seen that she had 30 days left on her lifespan. Several Goth ancestors share this quirk.
Frida's facial appearance has changed little between The Sims 2 and The Sims 3. The overall facial structure is gaunt, the nose is slightly crooked/aquiline and her shoulder-length hair is still quite in disarray. Her eyes, on the other hand, were brown in The Sims 2 and blue in The Sims 3 (however, this could be because she was a ghost in The Sims 3 and the rest of her features are uniformed in pale blue). According to SimPE, her hair was black before it turned grey, meaning that she may have dyed it in The Sims 3: Supernatural.
She wore a violet blouse and cream colored pants in The Sims 2, but had a more elegant attire in The Sims 3, wearing a (vaguely) violet calf-length sleeveless dress, a watch on her left wrist and crocodile skin shoes.
