draw (0,0) -- (1,0);
draw (1,0) -- (1,1);

draw (0,0) -- (1,0);
draw  -- (1,1);

draw (0,0) -- (1,0) -- (1,1);

documentclass[tikz,border=5]{standalone}
usetikzlibrary{intersections}
tikzset{%
  from end of path/.style={
    insert path={
      pgfextra{%
        expandafterpgfprocesspathextractpoints%
          csname tikz@intersect@path@name@#1endcsname%
        pgfpointlastonpath%
        pgfgetlastxylastxlasty
      }
      (lastx,lasty)
}}}

begin{document}
begin{tikzpicture}
draw [name path=A] (0,0) -- (1,1);
draw [red, from end of path=A, name path=B] arc (180:0:1);
draw [green, from end of path=B, name path=C] -- ++(0,-1);
draw [blue, from end of path=C] .. controls ++(0,-1) and ++(0,-2) .. (0,0);
end{tikzpicture}
end{document}