Most ERISA LTD group policies actually require that you apply for SSDI benefits.  If you win your SSDI claim, the insurer will likely reduce the amount of benefits that it pays to you.  Though it is not fair, generally, insurers are allowed to do this.

Be aware of potential double offsets.  Sometimes, individuals are covered under two or more LTD policies.  If both provided for an offset of SSDI benefits, that can result in a double offset and you receiving less disability income than planned.

For example, if you had two LTD policies that each paid $2,000 per month, you would expect $4,000 of monthly disability income.  If each policy provides for an SSDI offset, and your SSDI benefit was $1,000 per month, courts have ruled that the insurer may take an SSDI offset from both policies, thus, the insured is left with $3,000 in monthly disability income–$1,000 from each LTD policy, and $1,000 from SSDI.