1. CVA can result in myocardial necrosis, ecg changes and even chest pain through activation of sympathetic system, type II MI rather than acute plaque rupture.

2. embolic phenomenon: dvt with PFO, afib, can result in coronary and cerebrovascular embolism

3. large MI resulting in low cardiac output that will worsen hemodynamically significant carotid disease. similarly hypertension during MI causing cva

4. plaque dislodging during catheterization 

I would add aortic dissection.

Transoesophageal echocardiography, CT thoracic angiogram or magnetic resonance imaging would help.

Have a look at the attached paper

May be less common, but if still unexplained can consider hypercoaguable states, vasculitis, substance use (cocaine, vasospasm) and/or endocrinopathies (pheo causing sudden elevations in blood pressure, cortisol/ACTH secreting tumors, etc)

On several occasions, I have seen this. In each case the patient had a large anterior STEMI that went undetected - either the patient was relatively asymptomatic and didn't seek medical attention or ignored the symptoms. The CVA occurred 2-5 days later and we speculated was caused by dislodgment of LV thrombus that formed after the MI and resulting apical akinesis. The troponin trend can be helpful to make this diagnosis. For example, if the troponin is already high and/or downtrending without significant upward slope then this is probably the case. 

Today in our centre, a 40 year old man was admitted to cardiology department   for left sided chest pain, headache and neck pain. He had ST-T changes on  ECG. He was triaged  quickly for a coronary  angioram. Post- procedure he suffered deteriorating consciousness. CT head revealed central large subarachnoid haemorrhage. My colleagues had to reverse his heparin dosage given in angio. He was transferred for neurosurgical intervention

Learning lessons:-

History  taking and examination are very important. It is also common to find ST- T wave changes in subarachnoid haemorrhage.

I would look at embolization. 

In our neurovascular clinics. We always ask for ECGs for cases of  Transient Ischaemic attacks. There is a strong association between AF, IHD and stroke / TIAs. Soit is  no wonder when patients have a heart and a brain attack in one go.

I have seen many patients having AMI and stroke  simultaneously or subsequently.specially following Extensive anterior MI usually due to dislodgement of LV thrombus,or may be due to same aeitiopathology of MI and stroke---Stress/HTN- plaque rupture-platelet aggregation in both brain and coronary artery/ even may develop hemorrhagic stroke due to rupture of cerebral artery spcialy weakened previously by atherosclerosis or aneurysm