The reference refers to the scalar retrieved via $a[0], not the array index [0].  The reference knows nothing about the array that scalar came from.  And the scalar will exist as long as its refcount is > 0.

$ perl -MDevel::Peek -E'@a=qw(a b c); $r=\$a[0]; Dump $r; @a=(); Dump 
+$r'
SV = IV(0xa95bc0) at 0xa95bd0
  REFCNT = 1
  FLAGS = (ROK)
  RV = 0xa77998
  SV = PV(0xa75c20) at 0xa77998
    REFCNT = 2                   <---
    FLAGS = (POK,pPOK)
    PV = 0xa8ee40 "a"\0
    CUR = 1
    LEN = 16
SV = IV(0xa95bc0) at 0xa95bd0
  REFCNT = 1
  FLAGS = (ROK)
  RV = 0xa77998
  SV = PV(0xa75c20) at 0xa77998
    REFCNT = 1                   <---
    FLAGS = (POK,pPOK)
    PV = 0xa8ee40 "a"\0
    CUR = 1
    LEN = 16
[download]

(note the refcounts)