The memory expansion firmware has the following code to test the size of the memory expansion card, if installed:

numbanks  equ   $03bb         ; screen hole - $c0
sizetemp  equ   $0478         ; screen hole shared
addrl     equ   $bff8         ; slinky address reg for indirect use
addrm     equ   $bff9         ; real registers are from $c0c0-$c0c3
addrh     equ   $bffa         ; ..
data      equ   $bffb         ; slinky data reg

; at entry x is expected to have $c8 (slot * $10 + $88)
; and y is expected to contain $c4 (slot $Cn)
testsize  equ   *
          lda   #0            ; zero address reg l/m
          sta   addrl,x
          sta   addrm,x
          lda   #$10          ; start at 1 meg and go down
          sec
tsloop    sbc   #1            ; move down a bank
          sta   addrh,x
          lda   data,x        ; save existing data
          pha
          dec   addrl,x       ; fix address (undo auto-increment)
          lda   #$a5          ; common apple check byte
          sta   data,x        ; store it
          dec   addrl,x       ; fix...
          eor   data,x        ; 0 if the data is there
          dec   addrl,x       ; fix...
          cmp   #1            ; C = 0 if data okay
          pla
          sta   data,x        ; restore data
          lda   addrh,x       ; <-- SEE COMMENTS BELOW
          and   #$0f          ; only lower nibble valid
          beq   tsnoram       ; no RAM somehow!
          bcs   tsloop        ; loop until we find a bank
          adc   #1            ; C = 0 from compare
tsnoram   sta   numbanks,y
          lsr   a
          sta   sizetemp      ; sizetemp = upper byte of block count
          rts

If you note the code starting at the indicated line, you can see that the code grabs the high byte of the Slinky address register and uses the low nibble directly as a counter value.

The problem is that when there is no memory expansion card installed, there is no register, and the value there is floating bus. The only reason the code gets out of the loop is because the floating bus happens to usually have a bunch of bytes streaming by that have 0 in the low byte.

That being said, the current MAME does not float the bus for $C0C0-$C0CF. This results in ROM $03 hanging when the card is first accessed, and, due to changes in in ROM $04, hang at boot for ROM $04.