There actually is a company that made an adapter to make this possible.
It would take a regular PCI slot and be able to run a 1x PCIe device in it like an Network card or a Sound card. Maybe a GPU would be fine if only used for mining.
However the adapter is expensive, usually costs more than a new motherboard and not cost effective.
Yes, we can find that kind of adapter on the market.
One of my friends has bought it (PCI to PCIe 1X adapter). Its price around $40, planned use for mining, but I didn't yet hear back about the result.