Can an entrapped nerve be cured?

Nerve entrapment: In most cases, yes, depending on the cause & the location. For example, if the cause is obesity, weight reduction is the goal. If by compression on the nerve, surgical intervention is done, etc.

Yes: Surgical release may resolve symptoms

Yes, but: Since this varies so much in terms of location, chronicity, severity, and co-morbidities, need to be more specific regarding the situation, so your question can be answered with more clarity.