Well, if the business model is reselling FAANG talent at a discount to FAANG prices, this can and should happen. If you’re reselling FAANG talent you should be doing it at a premium to FAANG prices.
Some contracts include contract-to-hire provisions. In other cases, b/c of the total value of the customer relationship, the cost of the customer poaching is just a cost of doing business. Other times, a small contacting firm is stuck between a rock and a hard place - there's nothing they can do about it. It sort of varies.
However, I don't think lack of executive awareness is the issue.
Yes, this happens and one cannot do anything about it.
Don't feel bad, that's how the world is..
Most agencies don't have talent capable of interviewing and getting accepted at FAANG. That doesn't mean they can't do FAANG work, even at my current company, the interview was way harder than the actual job itself.