If you no longer have an HSA-qualified health insurance plan, you can't make contributions to your HSA.
However, HSA usage is not defined by eligibility. While you can no longer contribute to your HSA if you don't have an HSA-qualified health insurance plan, you can still invest or pay for qualified out-of-pocket medical expenses with your HSA funds.
An HSA is truly a lifetime savings account that is always there for health expenses. HSA eligibility does not hinder this HSA benefit.