To all US readers. READ your policy. Look for the "claw back".
My brother had a LTDP. The "claw back" was that for every dollar he got from Social Security Disability, the policy would "claw back" the same amount. Also, if Social Security Administration denied his disability claim, the LT policy would not pay anything.
You should definitely ask for the actual insurance documents and make sure you know what you're getting and that you're comfortable with the coverage you have. In my experience, work policies usually have some significant gotchas and you may or may not want a supplemental policy. Other things to look out for:
Own occupation or
any occupation - Walmart greeter anyone?
Payout period - Some policies only pay out for a certain amount of years
Definition of disabled - Who determines whether you are disabled or not? SSA? A review board? Your doctor?
Partial disability coverage - This is good if you have a reduced ability to work or a slow recovery period.
How long is long? - How long do you need to be disabled before benefits kick in?
COLA - Cost of living adjustments or fixed payout?
Amount - Percentage of income, limits, etc?
IIRC, my work policy covers so many years of disability for my own occupation at 60% of my income, but after that it switches to any occupation and I believe there's a maximum number of years it will pay out for, 5-10 I believe. An insurance review board determines my disability status. On the other hand, my personal policy covers up to a set amount of my income that I chose, less the amount that SSDI or other policies pay out. That's pretty typical AFAIK, but definitely evaluate your needs accordingly. It is my own occupation forever, pays out until full retirement age with cost of living adjustments, and disability is determined by my own personal doctor. It kicks in after 3 months and also covers partial disability where I have a reduced ability to work. As I get closer to FI, I can reduce the amount I am insured for until I drop it when I no longer need it, but in the meantime I should be covered even if SSA denies my claim or I run out of my work benefits.