While $0 is used to neat effect its associated perl5 MAGIC is not used, and I quoth from the source

# Turn off special $0 magic

*0 = \ my $zero;
[download]

After that $0 will loose it's magical behaviour e.g

shell> perl -MDevel::Peek -
Dump $0;
*0 = \ my $zero;
Dump $0;

^D
SV = PVMG(0x99900b0) at 0x999410c
  REFCNT = 1
  FLAGS = (GMG,SMG,pPOK)
  IV = 0
  NV = 0
  PV = 0x99950e8 "-"\0
  CUR = 1
  LEN = 2
  MAGIC = 0x99950f8
    MG_VIRTUAL = &PL_vtbl_sv
    MG_TYPE = PERL_MAGIC_sv(\0)
    MG_OBJ = 0x9994100
    MG_LEN = 1
    MG_PTR = 0x9995118 "0"
SV = NULL(0x0) at 0x9997828
  REFCNT = 2
  FLAGS = (PADBUSY,PADMY)
[download]

Although leaving $0 scrubbing out could certainly lead to some interesting debugging facilities in conjunction with top ;)