Pulmonary Embolism (PE): Given the patient's sudden onset of chest pain and hypotension, along with a background of aplastic anemia which may predispose to thrombotic events due to potential imbalances in blood components, PE is a highly plausible diagnosis. The patient's age and immobility due to dementia also increase the risk of venous thromboembolism.

Myocardial Infarction (MI): Although less common in the context provided, MI should be considered, especially in an elderly patient with sudden chest pain and hypotension. The presence of dementia and aplastic anemia does not exclude cardiac causes of chest pain.
Pneumonia: Elderly patients, especially those with dementia, may not exhibit typical symptoms of pneumonia. Sudden onset of chest pain and hypotension could be indicative of severe pneumonia, particularly if there's an associated sepsis.
Aortic Dissection: This is a less common but critical diagnosis to consider in any patient presenting with sudden chest pain. The hypotension could be due to involvement of the aortic valve or rupture into the pericardial space.

Cardiac Tamponade: Although rare, cardiac tamponade can present with hypotension and chest pain. It's crucial to consider, especially if there's a history of malignancy or recent cardiac procedures, though the provided history does not strongly suggest this.
Tension Pneumothorax: This is a life-threatening condition that requires immediate recognition and treatment. It could present with sudden chest pain and hypotension, especially in the context of mechanical ventilation or barotrauma, though the scenario does not specifically suggest these.
Massive Hemorrhage: Given the patient's aplastic anemia, any bleeding could be catastrophic. A sudden drop in blood pressure with chest pain could indicate internal bleeding, which would be exacerbated by the patient's underlying condition affecting blood cell production.

Pulmonary Artery Rupture: This is an extremely rare condition but could be considered in the differential diagnosis of sudden chest pain and hypotension, especially if there's a history of pulmonary artery catheterization or other pulmonary conditions.
Spontaneous Esophageal Rupture (Boerhaave's Syndrome): Presents with severe chest pain and can lead to hypotension due to associated mediastinitis or sepsis. It's a rare condition but should be considered in the differential of acute chest pain.