Then how did they recover? If your body has no antibodies to the virus then why would the virus ever stop spreading within you?

Antibodies are produced by the humoral arm of the immune system, but there is another arm:

https://en.wikipedia.org/wiki/Cell-mediated_immunity

Basically this other arm tells infected cells to kill themselves, and they comply.

This is an artefact of the current antibody tests, which mostly only sample a response to a single antigen. Which viral proteins you mount a response against will vary from individual to individual. To really know if you have no antibody response you need to test for a response to multiple antigens.

The cells that generate the antibodies may die later.