It does not make sense to provide passport of the country where you escaped persecution and settled down to the foreign country as a asylee. btw travel document will let you travel to other foreign countries too but you have to go through the normal visa process.
You are asking for refuge in the host country fearing persecution from the home country. You have been given refuge here. Now, why would you want the passport from the home country renewed? YOu have provision for travel with the travel document to any country provided that you follow the visa procedure. With the home country passport, I guess you want to travel back and maintain properties there which totally fcuks up the asylee case in the host country. Anyway, idk if its fake or real or whatever the case might be. once you have refuge in the host country, the validity of the home country goes down the drain. Considering your refuge in the host country, now why would the home country want to give you passport and stuff?