What happens when a company splits?

So, apparently Ebay's stock plummeted this weekend by nearly 50%. I did some quick research on the matter and it appears to have been caused by the fact the they just split from PayPal, which will now be traded under its own symbol.

This just made me wonder; what happens with shares after a split like this? Do the people who owned Ebay stock just have to deal with a 50% loss and be done with it, or will they receive any shares of PayPal stock as compensation? Or does something else happen?

Hope someone here will tell me.

And note that this is different from the more traditional "Stock Split" like Apple did a while back. When that happened, if you owned 100 shares of AAPL at 700, suddenly you owned 700 shares of AAPL at 100. (round numbers for simplicity). Bottom line, nobody loses money on a stock split or and company divestiture like you mentioned with EBAY. The odd stock splits do make for some crazy option strike prices!

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John Bradford said: ↑
And note that this is different from the more traditional "Stock Split" like Apple did a while back. When that happened, if you owned 100 shares of AAPL at 700, suddenly you owned 700 shares of AAPL at 100. (round numbers for simplicity). Bottom line, nobody loses money on a stock split or and company divestiture like you mentioned with EBAY. The odd stock splits do make for some crazy option strike prices!
Thanks for the excellent explanation, it cleared up pretty much all questionmarks.
But you just said something interesting, you mentioned that stock splits make for opportunities for trading with options. This is pretty much new to me, so would you mind telling me a bit more about this subject? Like, just as an example, how could options have let me profit of this case of Ebay splitting? =)

It doesn't make any options opportunities...just makes for weird strike prices for awhile as option positions are split as well. So a 3-1 regular split would turn a 107 strike into a 35.66 strike or 35.67 depending on how they round. There is no arbitrage or way to game the split.

Acstudio said: ↑
It doesn't make any options opportunities...just makes for weird strike prices for awhile as option positions are split as well. So a 3-1 regular split would turn a 107 strike into a 35.66 strike or 35.67 depending on how they round. There is no arbitrage or way to game the split.
Oh, ok, that's a bit disappointing. Either way, thanks.