What happens if a respondent who is not the DPP in the criminal case dies?

If a respondent who is not the DPP in the criminal case dies, the appeal shall abate, see section 386 of the Criminal Procedure Act, 1985. 

Note: Also that; according section 371 of CPA every appeal from a Subordinate Court shall finally abate on the death of appellant. However according to the same provisions appeal from a sentence of a fine does not abate on the death of appellant.