In my system, socks have only one place they belong: in the drawer of their owner's dresser.
So the strays go there, where they will eventually meet up with their mates, with no extra effort.
It's so much easier than having a sock basket to accumulate them.
They go to the drawer in the same trip as all the others. And they get matched up in the drawer.
What makes this even easier is that I don't sort socks when I'm folding--well, that's not true, but I don't -mate- them--I just put each person's socks in a pile and stuff them in the drawer. When someone gets dressed in the morning, they rummage through to find a pair.
I make it even easier by buying each person many pairs of the same socks. Only one brand of black dress socks, of tan dress socks, of white sweatsocks. So if you lose have of pair A and half of pair B, you still have a pair. Helps when they rip too.