PCIe x8 bus w/ x16 card

Only if the card fits. There are some logic boards that have x8 slots with x16 connectors, but I don't know if your 'Poweredge 2950' has one such connector available.

Logically, the card and the socket will negotiate to use the available lanes.

Physically, the socket can be cut open ended, or the card can be slotted, as long as it is OK to just ignore the additional lanes.

There are 1x and 16x quad video cards, but no x4 and x8.

If there are motherboard components in the way, cutting the socket does NOT make the new card fit. It is common practice for an x8 motherboard to have an x16 socket in order to allow card selection flexibility.

The x8 slot is on a riser, no other component, fortunately. No x16 option for this motherboard, unfortunately.