To claim disability insurance you must be unable to work but willing. To claim unemployment you must not have a job but must be in a health condition suitable for a job as soon as you get one. Since both are in contradiction, you may contact your local attorney to help you in this regards. So, can you file for medical disability while collecting unemployment benefits? The answer would be a little tricky. It largely depends on the kind of work that is defined in the programs. Disability insurance is not directly connected to Employment Security Commission. This might be reason enough for you to file for medical disability while collecting unemployment benefits. However, when you file for unemployment you make an unspoken statement that you are ready and available for work (full time) and are willing to find jobs that suit you. On the other hand when you filed for disability, you state that you are unable to work (at all) due to a disability.
These two conditions have a huge disparity between themselves and hence it might be a problem if the Employment Security Commission finds out that you have filed for disability benefits while on unemployment benefits. You may not know but there can be various ways by which the Commission might get to now of this dual benefit that you are receiving.
If you are caught receiving and accepting both benefits, then you will be required to repay all unemployment / disability benefits because you will not be eligible. You could also be charged with fraud.