If you were the last one on Earth, you could replicate yourself using Adam’s Replication Process: pull a rib from your body and make an opposite-gender clone of yourself. You could then have sex with your clone. If incest produces messed-up genes, I imagine then procreating with your cloned rib must make for some exceedingly messed-up kids. And mind you, to continue the human race, these kids would have to reproduce with each other. So the human race would continue, but it would be a very genetically messed up, in bred version of itself.