For "regular" dilution, the way it works is that there's a pre-money and post-money valuation. If a company is worth 1M pre-money, and an investor puts in 1M, then the company is worth 2M post-money. Someone who owned 1% before (effectively 10k of the pre-money) now owns 0.5% (effectively 10k of the post-money). Ostensibly, their stake should be worth exactly the same before and after the deal, a smaller slice of a bigger pie. In practice, there's various incentives to inflate valuations, such that the early investor's slice is getting smaller faster than the pie is getting bigger.
Furthermore, investors tend to demand extra terms on top. The big one here is called liquidation preference, which is a clause that says, approximately, if/when this company is sold, this investor gets the first X amount of it, usually corresponding to some multiplier of their investment amount. Later rounds will ask to win out in preference, effectively creating a stack of liquidation preferences. In practice, liquidation preferences can often add up to so much that a moderately-successful sale goes entirely to preferred shareholders, and common shareholders see nothing. Perhaps the dealmakers put in a bit of a sweetener for the founders and/or current executives to grease the deal. Your average employee and angel or seed investors certainly see nothing in this deal.
The problem is with the first step. If the angels owns 1%, and the founders own the other 99%. When taking more money, it should be the founders selling a portion of the 99%, not diluting the angles percentage.
The stake should remain the same, but double in value. That's the risk of early investment being paid out.
The actual transaction is framed in terms of generating more shares in the company, such that existing shares represent an ever smaller piece of the total pool. What you're suggesting would be the founders selling a fraction of their shares to the new investors, while keeping total shares the same. Institutional investors are highly opposed to that, for a variety of reasons, including because they want founders to remain bought in to the company. (Some institutional investors will allow founders to "take some money off the table" to a small extent, but that's the exception and not the norm, and it's viewed as a favor to the founders. More cynically, institutional investors don't want founders to have financial independence before the company fully succeeds.)
The edit window has passed, so I'll add a new reply.
The other thing to keep in mind is that institutional investors will generally insist that founders earn out their stake via vesting over, say, 4 years. Then, the founders' stake, despite being earmarked for them, aren't officially theirs yet.
On top of that, as long as the preferred investors get their slice they don’t care if common stock gets fucked over. There can be side deals where the buyer will “buy” the company for a lower price but gives the founders a huge salary and/or shares in the buying company.
For example, lets say a company is valued at 100mil with 50mil in preferred stock and 50mil in common stock where the preferred stock is owned by institutional investors and everyone else (including founders and angel investors) has common stock. Lets say there are two founders that own 10% each, an angel which owns 10%, and an employee options pool with the remaining 20%.
Now lets say there are two scenarios:
1. The company is sold for 90mil, 50m goes to preferred stock, and the remaining 40m goes to the common pool — 8m to each founder and angel and 16m to the options pool.
2. The company is sold for 50m, but the founders each get a salary of 5m for 3 years. The preferred stock gets the entire 50m. The angel and employee pools get 0, and the founders get 15m each.
In scenario 2 the preferred stock gets their share, the founders come out ahead by 7m each, AND the buyer has to pay 10m less than option 1. But the angel and employees get shafted.
The question then becomes why scenario 2 wouldn't be a major breach of fiduciary duty, and why common stockholders don't sue over it and/or regulators don't pursue it.
Furthermore, investors tend to demand extra terms on top. The big one here is called liquidation preference, which is a clause that says, approximately, if/when this company is sold, this investor gets the first X amount of it, usually corresponding to some multiplier of their investment amount. Later rounds will ask to win out in preference, effectively creating a stack of liquidation preferences. In practice, liquidation preferences can often add up to so much that a moderately-successful sale goes entirely to preferred shareholders, and common shareholders see nothing. Perhaps the dealmakers put in a bit of a sweetener for the founders and/or current executives to grease the deal. Your average employee and angel or seed investors certainly see nothing in this deal.