Suppose on exchange X, BTC/USD trades at 12000, on exchange Y, BTC/USDT at 10000. You sell an expensive BTC on X (for 12000 USD), you buy a cheap BTC on Y (for 10000 USDT).

Now they nicely converge to 20000. You buy back a BTC on X, giving you a loss of 8000 USD. You sell a BTC on Y, giving you a nice 10000 USDT gain.

So, you realised and locked in the projected 2000 USD arb profits - oh, assuming the 10000 USDT you got on Y can actually be exchanged for 10000 USD. You have exposure now to USDT/USD, and your arb profit (in USD) depends on that cross.