How do agencies with FAANG clients keep staff from leaving for FAANGs?

I'm an engineer at an agency in the Midwest. We have a FAANG as a client. I like my current company, but since I'm always assigned to projects for the FAANG, which I enjoy — and since FAANGs of course pay their employees very well — I decided to apply for and was offered a job there. (Contractually our clients can't "poach" us, but we're free to apply wherever.)

As I say my good-byes, when other employees learn where I'm going they sound very interested in applying, themselves. I feel a little bad about starting some kind of exodus, since the agency has treated me well. My boss didn't really even counter-offer since he admitted that the agency can't hope to compete with FAANGs.

This makes me curious — how do agencies/consultancies prevent this from happening?

Of course some employees will prefer agencies for various reasons, but the benefits and pay of big tech companies are really appealing, and far beyond what most agencies could afford.

Are executives aware that this is a risk when they win a contract with a FAANG?