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She and her husband never appeared alive in The Sims Series. Prudence along with Victor, Gretle, and Simon were featured in the family tree of Mortimer Goth and existed to fill in as grandparents for Mortimer.
In The Sims 3, Prudence is already deceased, having died of old age. Her tombstone can be found in the Goth family graveyard along with that of her husband, her son-in-law's parents, and Lolita, whose relation with the family is unknown. Prudence wears a lilac sweater with a red skirt, and has grey hair which is tied into a bun. Between The Sims 3 and The Sims 2, her grave disappeared from the Goth graveyard. It is possible that a fire burned down the house and destroyed her and Lolita's grave, considering that Gunther and Cornelia Goth died in two separate fires.
Prudence is now long dead, and is likely buried in either the Goth Sr. graveyard or the graveyard of the younger Goth Family. She doesn't technically appear, but it is presumed that she exists due to her previous appearance in The Sims 3.
Life leading up to The Sims 2
As in previous appearances, Prudence is still deceased. Despite this, Prudence's tombstone can not be found in the Goth family graveyard, nor can it be found anywhere else. Therefore, it is presumed that her tombstone was destroyed by someone, or that the creators of the game made a "grave mistake" similar to Frida Goth's situation.
She has the same hairstyle as she did in The Sims 3, and wears a blue cardigan with cream colored pants. She bears a strong resemblance to her daughter Miss Crumplebottom's appearance in The Sims: Hot Date, as well as her distant relative Mrs. CrumpleBottom in The Sims 2: Nightlife. According to her SimDNA in SimPE, Prudence's hair was black before it turned grey. According to her age data, she had 26 days in the elderlife stage, when she died.