The answer to this question depends on if your long-term disability insurance policy is governed by ERISA. If you obtained your disability policy as a benefit from your employer, then it is probably governed by ERISA.
In most ERISA disability policies, an employee is only eligible for disability benefits if they become disabled while they are actively employed. Active employment is usually defined in the disability policy as working a minimum of 25 hours per week.
If an employee is terminated or quits, but can prove that he or she was disabled at the time of the termination or resignation, then he or she should be eligible to collect long-term disability benefits.
If you are working with a disability and think you may be fired, make sure you document all of your restrictions and limitations with your treating physician and your employer prior to being let go. Many employees are reluctant to advise their employer of a disabling condition as they fear that they may be fired and then the disability insurance company will deny their claim, but you should at least alert your doctor to your condition. Claimants who have a legitimate disabling condition and the support of their treating physician should have their claim for long-term disability benefits approved.