How do pools handle splits?

[MentalNomad]

For example, I'm mining at ethermine. I'm going to mine through the Byzantium fork, which happens shortly.

I have a balance due and payable every time i hit 1 ETH... which means I'll have a "due balance" when the fork hits.

Presumably, some time later, my balance will reach 1 ETH and I'll get a payout...

If the fork had, indeed, caused a chain split (which won't happen this time, but let's just discuss what would happen if it did), will the pool pay out my held balance to both chains? Or will only pay out to a "primary" chain, and keep the mined & unpaid funds on the alt chain?

[MentalNomad]

I suppose that, after the split, I'd only be mining to one chain or the other - whichever the pool followed - so only that "unpaid balance" would grow and hit my payment threshold.

But I'll still have, say, .5 ETH of "unpaid" balance on the other chain. How did pools handle this effect on, say, the BTC/BCH split?