Late stage esophageal cancer, has mestastasized across lympth nodes, & into stage 4 liver, getting chemo now, how long can the person hopefully live?

Undetermined. One day at a time. Although statistics can inform you what happened to other people with similar problems, ultimately how long a you are expected to live is speculative and unpredictable. Ultimately, if you are alive today, you are alive today.
Guarded prognosis. Chemo_radiation is usual treatment for stage 4 disease for palliation few do respond, most important to make as comfortable as possible, pain management, endo esophageal stents help to swallow prevent aspiration pnumonia, and hospice care.