Why does this remnant exist? It's not because they earned it, but because God freely chose them.
The verse states this remnant is 'chosen by grace.' This is a critical distinction. The mass of the Jewish people at the time were relying on their own adherence to the Law, their heritage, and their 'works.' But this remnant is set apart not because of anything they did, but because of God's unmerited favor – His grace.
Paul emphasizes that grace and works are mutually exclusive. If salvation were based on our works, it would be a debt God owes us. But because it's based on grace, it's a free gift. This means God's choice isn't based on foreseeing who would be 'good enough,' but on His own sovereign, gracious purpose.