I'm a little unclear on the question. In the US, it is the parents responsibility to set everything up so that their estates is passed to their children.
A word of advice. We just went through this with my husband's mother passing and it was a nasty mess. Be sure they leave a clearly written will and that their estate is in good order with clearly written instructions.
Also (in the US) Income taxes will still need to be filed for the last time for the deceased.
You can prepare by asking your parents if they have a will and if they need any assistance in record keeping....it will save a lot of time and angst if things are in some order.