documentclass{article}

usepackage{pgfplots}

begin{document}
    begin{tikzpicture}
        begin{axis}
            [
                % I'm using this:
                yticklabel = {pgfmathparse{tick-130}pgfmathprintnumber{pgfmathresult}},
                y filter/.expression = {y + 130},
                ymin = 0
                % I would like to have this:
                % comb origin = -infty % or something
            ]
            addplot[ycomb] coordinates {
                (1, -6)
                (2, -80)
                (3, -85)
                (4, -120)
                (5, -120)
                (6, -120)
                (7, -120)
                (8, -120)
                (9, -120)
            };
        end{axis}
    end{tikzpicture}
end{document}