It would be a Ponzi scheme if the annual total of dividends exceeded the annual total of profits.
Check the annual filings to see if that's happening.
Otherwise, they're paying dividends out of profits and raising working capital in the secondary market.
Why not just use the profits as working capital, like most public (and private) companies do? Because by law if they don't pay out at least 90% of annual profits as dividends, they have to pay a higher tax rate.
It doesn't make sense to do that when they can distribute the profits as dividends and sell more shares at the same time.
The side effect of that is that it keeps their stock price low, which makes their yield look huge. The low price for a huge yield attracts investors, meaning they can sell more shares, and end up with a lot more working capital than if they just kept the profits in-house.
Which means they can expand the whole operation, making it more stable by dint of diversification, as long as the things they invest in are stable.
I believe the banks and the feds are acting right now to make only high-quality loans, in order to balance out the risk pool overall. It would explain the widely reported difficulty in obtaining a loan even though rates seem to be screaming "borrow me."
Which is great for AGNC. The less iffy paper they buy, the better. If they focus on good loans, and they hedge variable rates on money they borrow (look up "swaptions"), then there is very low risk of a total collapse. But if they're up to their eyeballs in junk mortgages and other people's mistakes, there could be trouble coming.