The OEM versions of previous Windows that upgraded tended to tie themselves to the motherboard. If you have a retail copy then you can reuse your key with no issues. The person who got your old PC would need their own key to activate Windows.
I originally had a win7 retail disk which i upgraded to win10. I use a win10 iso on a stick to install win10 now. It never asks for a code. So it seems that someone else could then install the win10 that is linked to the motherboard without a code.