\version "2.22.2"

#(define*-public ((box-grob-stencil-with-thickness #:optional (thick 0.1) (pad 0)) grob)
  (let* ((xext (ly:grob-extent grob grob 0))
         (yext (ly:grob-extent grob grob 1))
         (xext (interval-widen xext pad))
         (yext (interval-widen yext pad)))
    (ly:stencil-add
      (make-filled-box-stencil (interval-widen xext thick) (cons (- (car yext) thick) (car yext)))
      (make-filled-box-stencil (interval-widen xext thick) (cons (cdr yext) (+ (cdr yext) thick)))
      (make-filled-box-stencil (cons (cdr xext) (+ (cdr xext) thick)) yext)
      (make-filled-box-stencil (cons (- (car xext) thick) (car xext)) yext))))

\score {
  \layout {
     \context {
       \Score
       \override System.stencil =
         #(box-grob-stencil-with-thickness 0.4 0.5)
     }
  }
  {
     \slurDown c4 ( g4  c''4)
  }
}

\markup\vspace #1

#(define-public (box-grob-stencil grob)
   (let* ((det (ly:grob-property grob 'details))
          (thick (assoc-get 'box-thickness det 0.1))
          (pad (assoc-get 'box-padding det 0)))
     ((box-grob-stencil-with-thickness thick pad) grob)))

\score {
  \layout {
     \context {
       \Score
       \override System.stencil = #box-grob-stencil
       \override System.details.box-thickness = #1
       \override System.details.box-padding = #1
     }
  }
  {
     \slurDown c4 ( g4  c''4)
  }
}