This is interesting because I imagined the whole purpose of this insurance was for relatively young people who have a risk of becoming disabled and not being able to work or having any savings yet etc. So low probability and high consequences.
That would be long-term disability insurance. Long-term disability allows you to get your salary or a portion of your salary if you become ill or have an accident that makes it unable for you to work. Short-term disability coverage is for the time between when you first can't work and when the long-term disability insurance kicks in.