Michelle Sharkey worked for a Lloyds branch in Huyton, Liverpool, and transferred 14 separate amounts from the victim, believed to have been in her 60s, who has since died, a court heard.
The 53-year-old pilfered exactly £11,675 from the victim's finances, knowing her client was vulnerable because of her chronic drink addiction, Liverpool Crown Court heard.
Sharkey controlled two accounts relating to the victim and moved money into her partner David's account, and also Irene Dennett, her elderly mother.
The Lloyds employee "laundered and moved the cash in a triangle," from one account to another, defrauding the victim, who knew about the crime before she died, said Gerald Baxter, prosecuting.
Sharkey, who had no previous convictions, carried out the fraud between February 2017 and January 2018.
It was a "gross abuse of her power", said Mr Baxter. He said she had carried out the fraud over a sustained period of time on a client who led a "chaotic lifestyle" because of her addiction.
Sharkey, who pleaded guilty, left the bank account overdrawn and used the stolen cash as her position as the sole breadwinner in her own family.
Anna Duke, defending, said Sharkey had worked for the bank for a considerable period of time and "was not thinking properly" when she plundered the customer's funds.
Sharkey had found herself in "dire straits" financially.
Miss Duke told Judge Neil Flewitt: "She didn't want to let her family know of the dire situations, instead of speaking to her family, [telling them], with the benefit of hindsight, 'this is the situation, we can't cope'."
The court was told some of Sharkey's friends and family had now disowned and "ostracised her", but there were some relatives at the back of court, who broke down in tears as she was handed a 12-month prison term.
Miss Duke added: "She attended the police station and made complete submissions. There is genuine remorse in relation to what she has done and the predicament she has found herself in."
Judge Flewitt decided he could not suspend a prison sentence, telling Sharkey's barrister: "There is strong public interest in people knowing that when they put money in the bank, it is safe."
The court heard it was accepted Sharkey did not lead a "champagne chalice lifestyle" and did not go on luxurious holidays, instead spending the money on day-to-day living to keep the roof over her family's head.
Miss Duke said her client, of Asaph Drive in Warrington, was suffering depression at the time of her crimes, and had since contemplated suicide on an almost daily basis.
Gerald Baxter, prosecuting, said that Sharkey had fully repaid the amount she stole, taking it from her own pension funds.
Judge Flewitt said Sharkey left her victim's balance "close to nil", and her crimes involved "some thought and planning".
He added: "It is undisputed this was an abuse of a position of power and it was a significant position of responsibility you held.
"You have broken the trust of the bank. You chose the account of someone you knew to be vulnerable.
"People need to have confidence in those who manage their financial affairs."
