If a client dies and owes a balance, does he have to file?

The Personal Representative of his estate is supposed to file.

Since he is dead, he doesn't have to file ----------------- but the person handling the estate kinda needs to take care of that kind of stuff.

Does the person administering his estate have to file a final return?  Yes.

Does the tax have to be paid?  That depends on whether there are any assets, and any claims that have priority over taxes.  

Yes. If they worked or had a business running for that year, that return must be filed and marked that the client has passed. 

The personal representative of the estate, such as an executor or administrator, is responsible for filing the final return. If there is a surviving spouse and no personal representative has been appointed, the surviving spouse may file a joint return for the year of death.

E-filing doesn't work from purgatory, but it might from the hot place.

Otherwise, it's paper-filing for you.