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The trust said it “apologised unreservedly” to the patient’s family.
The ombudsman, Marie Anderson, described it as a “sad case”.
She said the patient’s limited chances of survival from her illness, liver disease, were dependent on her receiving timely and appropriate care.
In a statement to BBC News NI, the NHSCT said the patient’s treatment had fallen short of the accepted standard.
“We have apologised unreservedly to the family of the patient that the treatment and care she received fell short of the standard that we strive to achieve,” it said.
“We have identified and taken on board the learning from this case and this will continue to be reflected in practice going forward.”
The woman’s husband wished to remain anonymous but said he wanted his wife’s story to be told so lessons can be learned.
An investigation found there were “multiple failings” including a lengthy delay in carrying out critical tests and prescribing antibiotics, as well as inadequate nutrition and hydration during her time in hospital.
An examination of hospital records disclosed that the woman was not referred for review by a dietician until 10 days after she was admitted.
With regard to antibiotics, the woman’s husband said he had complained to the health trust that a check to see whether his wife had a bacterial infection was not carried out quickly enough.
An independent advisor informed the ombudsman that despite the patient’s ill health upon admittance to hospital, a vital procedure known as paracentesis, where fluid is taken from the stomach, was not performed until 12 days after the woman was admitted.
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While that procedure was not successful, notes show that doctors felt another attempt should be made, but the procedure was not carried out.
The investigation also found that the patient was not given an antibiotic until almost two weeks after admission. This was despite three potential sources of infection having been identified earlier and against a background of worsening liver failure.
Ms Anderson told BBC News NI that given the “serious failings”, her office has advised NHSCT to provide a £10,000 payment to the family in recognition of the upset, frustration and distress caused.
The Ombudsman suggested an apology be offered by the trust’s chief executive and each of the clinicians involved in the patient’s care.
In a statement, NHSCT said it had accepted the recommendations and issued a payment and an apology.