These hearings are not designed to benefit either party. They are designed to determine if you left your job for an approvable reason, or if you voluntarily quit for a personal reason or were discharged for a valid misconduct reason.
Really don't think there is a "three day" rule anywhere, as has been stated. At the unemployment hearing they will be looking at why the employer believed you had quit your job. No call no show is very hard to get around. Many places define a no call no show as an automatic reason for termination. However, my question is, did you call in before your shift began on either of these those two days and tell the employer you would not be coming in, or did you just not show up for two days and then call on the 7th hour of the second day and tell them where you'd been? If so, then at that point they told you you had been terminated, right? Or that they assumed you had quit, though you hadn't, right?
Did you have a doctor's statement for any of this two days absence?It would be good for your case if you or some member of your immediate family was in the hospital. We used to joke that a good reason for a no-call, no show is if you were in a coma. But it sounds as though you may have ended up incarcerated or in some other personal non medical position where you did not call or come to work for two days. Then when you did call, they said, "We assumed you had quit." They can certainly do this. Whether they are terminating you or "assuming you quit" is a moot point.
Your best defense would be to say that you were ....wherever you were, and were not able to call or come in to work. You did not have a family member or friend who could call in for you. However, you did contact your employer as soon as you were able. At this time, they told you you had been terminated, though you did not intend to quit the job and would have reported for work if you had been able to do so. If you had no prior attendance issues, you should mention this, as this would help your case.
If you have had many write ups or warnings for attendance issues, or if it is a handbook policy that a no call no show is an automatic termination, you will probably not win this case, even if the employer didn't even answer the phone for the hearing.
Also, now that you are entering treatment, you are not going to be "able and available for other work" until you are released from treatment, even if the claim is approved.