In many games where the protagonist is on the younger side, their parents often make an appearance, wishing them well on the start of their quest. For some reason, it's fairly common for the protagonist to only have one parent. While the fate of the absentee parent often turns into a major plot point in more story heavy games, there are many titles where the topic of the missing parent is not even broached.
In these cases, there's just an unspoken agreement that no one will speak of it. There might be the briefest mention that you were "just like him", which just raises further questions, really.
One of the few times this phenomenon is addressed directly is in Earthbound. Ness and his sister live with their mother. The father, in this case, does in fact exist however. Busy "working" far away, he only communicates with Ness over the phone, saving his game and dealing with his banking for him. Absent, but not forgotten.
Alternatively, many games have some variation on this, with the player's legal guardian being a grandparent, uncle, or some random adoptive parent. Again, the fate of the parents may or may not be relevant.