What is the criteria for a wife obtaining carer's allowance for husband with chronic illness

Carer's Allowance is a payment made to low-income people who are caring for someone who need assistance due to age, disability, or disease (including mental illness)

the term chronic means (of an illness)persisting for a long period of time or constantly recurring or of very poor quality
for your question it would mean something like "smokers" cough,recurring blood problems or any disease that is virtually difficult to become rid of
back pain that appears to be untreatable, arthritis are items of a chronic disease

You should speak to your Husband's Health care Provider and about his beneficiary's care plan.

call them

I'm sorry for your loss, but you would need to contact a lawyer in your area for the answer.