tikz rectangle with curved edges and inverted rounded corners

Question

I need to draw first a rectangle with curvy looking edges. Then I need a rectangle with curvy looking edges and also rounded corners. But the corners need to be inverted (pointing inwards). I have made a handmade drawing for illustration:

Answer 1

Note that I think I ought not answer 'do-it-all-for-me's such as this one. Also, be aware that I am much less likely to be responsive to follow-ups in such cases, unless your follow-up happens to appeal to me. If you want any adjustments, I therefore recommend that you desire the addition of one or more of the following:

1. one or more cats, sitting or lying;
2. one or more cauldrons;
3. one or more trams or single-decker buses.

---

\documentclass[tikz,border=10pt]{standalone}
\begin{document}
\begin{tikzpicture}
  \draw (0,0) coordinate (a) [bend right=15] to +(2,0) coordinate (b) [bend right] to +(0,-1) coordinate (c) [bend right] to (a |- c) [bend right=15] to cycle ;
  \begin{scope}
    \clip (3,0) coordinate (A) +(.1,0) coordinate (A1) -- +(1.9,0) coordinate (B1) arc (180:270:.1) coordinate (B2) -- +(0,-.8) coordinate (C1) arc (90:190:.1) coordinate (C2) -- (C2 -| A1) arc (0:90:.1) -- (B2 -| A) arc (270:360:.1) ;
    \draw (A) coordinate (a') [bend right=15] to +(2,0) coordinate (b') [bend right] to +(0,-1) coordinate (c') [bend right] to (a' |- c') [bend right=15] to cycle ;
  \end{scope}
  \clip (a') [bend right=15] to (b') [bend right] to (c') [bend right] to (a' |- c') [bend right=15] to cycle ;
  \draw   (B1) arc (180:270:.1)  (C1) arc (90:190:.1)  (C2 -| A1) arc (0:90:.1)  (B2 -| A) arc (270:360:.1) ;
\end{tikzpicture}
\end{document}

Answer 2

This is not a full answer unfortunately, but I needed a very similar shape: a rectangle with inverted corners, but not the convex edges. I made a shape (see here: myshape.tex) for it, in which the corners to invert can be selected:

The test script is rather small:

\RequirePackage{luatex85}
\documentclass[tikz,convert=false]{standalone}
\tikzset{
  shape example/.style={
    color=black!30,
    draw,
    fill=yellow!30,
    line width=.5cm,
  },
}

\input{myshape}

\begin{document}

\begin{tikzpicture}\Huge
  \node[rectangle with inverted corners, rectangle with inverted corners radius=20pt,
        rectangle with inverted corners selected={north west, north east},
        shape example, minimum height=6cm, inner ysep=1cm, inner xsep=.75cm] (s)
    {Rectangle with inverted corners\vrule width1pt height2cm};
  \foreach \anchor/\placement in
    {text/below, center/above, 70/above,
     base/below, base east/below, base west/below,
     mid/above, mid east/above, mid west/above,
     north/below, south/above, east/above, west/above,
     before north east/above, north east/below, after north east/above,
     before north west/above, north west/below, after north west/above,
     before south west/above, south west/above, after south west/below,
     before south east/below, south east/above, after south east/above}
  \draw[shift=(s.\anchor)] plot[mark=x] coordinates{(0,0)}
    node[\placement=0mm] {\scriptsize\texttt{(s.\anchor)}};
\end{tikzpicture}
\end{document}

'''