In　(Euzebio　et　al.,　2016　[10];　Chen　and　Tang,　2020　[8]),　the　bifurcation　diagram　and　all　global　phase　portraits　of　a　degenerate　planar　piecewise　linear　differential　system　＜(x)over　dot＞　=　F(x)　-　y,　＜(y)over　dot＞=　g(x)　-　alpha　with　three　zones　were　given　completely　for　the　non-extreme　case.　In　this　paper　we　deal　with　the　system　for　the　extreme　case　and　find　new　nonlinear　phenomena　of　bifurcation　for　this　planar　piecewise　linear　system,　i.e.,　a　generalized　degenerate　Hopf　bifurcation　occurs　for　points　at　infinity.　Moreover,　the　bifurcation　diagram　and　all　global　phase　portraits　in　the　Poincare　disc　are　obtained,　presenting　scabbard　bifurcation　curves,　grazing　bifurcation　curves　for　limit　cycles,　generalized　supercritical　(or　subcritical)　Hopf　bifurcation　curve　for　points　at　infinity,　generalized　degenerate　Hopf　bifurcation　value　for　points　at　infinity　and　double　limit　cycle　bifurcation　curve.　(C)　2021　Elsevier　Inc.　All　rights　reserved.