substitution

Hello mam, greetings of the day.
As per your query, if the objector dies during the execution petition for claiming order 22 rule 58 then, according to Order XXII Rule 10 it is the duty of the counsel representing the deceased party to inform the court as well as the opposite side of such death and bring the legal heirs of the deceased on record.  Till the, the court puts a stay order on the further hearing of the case until the probate court appoints an estate representative. As per your second question, Yes, even if the objector dies, the limitation act is applicable on him for certain period of time. The Limitation Act allows the actions in some cases where the injured party had not discovered the injury until after the standard date of expiration. As the objector has died during the case was on trial, he/she will get the benefit out of it.  
Hope this solves your query.
Regards
Nirali Nayak
Law Student