Can you collect disability insurance while recovering from surgery if you have been working for 35 years but are currently unemployed?

That would depend if you live in a state that provides disability insurance.

The type of disability insurance would also depend on the seriousness of the surgery, i.e. is it short-term, work injury related (workers comp); longer term, permanent (SSDI); private insurance (depends on the insurance policy). The Related Link below is an Excellent source for information on the above.