Just like any crypto currency, if you “cash” out BAT say for the american dollar USD, you are essentially trading in the BAT tokens for USD cash.
Meaning there still is 1.5Billion BAT available, but only 1 Billion is actually being traded/circulated and then 500M is being used as a user growth pool.
To put it simply: When you use cash (USD) to buy say 5 BAT at a market value of $0.37, You trade a total of $1.85 for 5 BAT, If BAT rises to say $1.00 a token, you can sell the BAT for $5.00. the BAT was simply traded not burned.
This principle is the same for tips/BAT earned from ads, etc.
If you get 10 BAT as a verified publisher you now own 10 BAT tokens, If you wish to “cash” out you are selling your 10 BAT back to Brave or whomever wants to buy the BAT (uphold for example) for your local currency, This means that uphold gets to keep your BAT and they pay you for the value of the BAT, still leaving 1.5b BAT total