Can this paph be saved?
 

I received this plant from a neighbor and I am new to orchid care. What can I do, if anything, to keep this plant alive? It had beautiful blooms!

Look up a technique called "sphag n bag" which will supply enough humidity until the plant has a chance to grow new roots.
Sphag-n-Bag

Are you sure it's a paphiopedilum? Sort of looks like a phalaenopsis to me. Either way I would probably put it in a zip-lock bag out of direct sunlight and when/if it starts to grow new roots I would pot it up. Welcome to the board and good luck.

Oh, yes, I forgot to say this looks like a Phal (Phalaenopsis) rather than a Paph (Paphiopedilum).

Welcome to Orchidboard!! :waving
That's definitely a Phal and not a Paph. To give it the best chance of survival I would cut off that spike before sphag-n-bagging it. It's an energy drain on the poor plant.

I agree with all above, it's a phal..
Yes, shag-n-bag is a good way of getting it to grow... Be careful to make sure you open the bag regularly to let air in and let it dry off a bit. If you get this right it should 'come back'! I killed a few phals at first from them being too wet with this method ...
what I found 'works' for me is putting the plant (bare root) in a plastic pot, with a bit of sphag around in the plastic bag. All enclosed but letting it breathe too...
Goood Luck! keep us posted.