We suggest that while Indigenous languages are threatened by capitalist and neoliberal encroachments, responses from applied linguists in the academy can be misguided. To make our argument, we must first define neoliberalism, and examine how the broader neoliberal discourses of choice, competition and the free market have percolated and distilled into local Indigenous language contexts, impacting languages, cultures and identities. We ask ourselves what identities are currently available, adopted and valorized by and for Indigenous language speakers, and how positions like Indigenous language speaker, academic/linguist, activist and teacher are altering in response to available neoliberal subject positions? We suggest that neoliberal discursive regimes position Indigenous peoples who do not speak their heritage languages as "victims needing recognition and redress." The result is that they have become trapped in colonizer ideologies viewing Indigenous peoples as unfit to govern themselves. Colonized now by neoliberalism, Indigenous language speakers forced to live within neoliberal regimes must adopt "identities of resignation," meaning engaged in a permanent struggle to accommodate themselves to the world. Instead, we posit that their positions are better framed and respected as identities of refusal, everyday actions of refusing enclosure.