Currently, pipeline build will fail automatically when the build is unable to communicate with the runner and we don't have a failover that will let the build run on the Bitbucket pipeline when this happens. Unless you manually remove the runs-on: in YAML to let Bitbucket pipeline know that you are not using runner anymore.
I like your idea of having a failover when a runner is offline to run on the Bitbucket pipeline so I have proceeded to raise a feature request on behalf of you at:
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