PCOPY is the easiest way I know to achieve the effect you're speaking of.
SCREEN _NEWIMAGE(800,600,32)
RANDOMIZE TIMER
'Create the persistent image
FOR I = 1 TO 100
LINE (RND * 800, RND * 600)-(RND * 800, RND * 600), _RGB32(RND * 255, RND * 255, RND * 255), BF
NEXT
'Now PCOPY that background to preserve it
PCOPY 0,1
'Now create the transient image and display it:
DO
PCOPY 1,0 'place background (no CLS needed)
X = X + 1: IF X > 800 THEN X = 0
LINE (X, 200)-STEP(200,200), _RGB(0,0,0), BF 'a black box for the colored background should show up nice for a transient image
_LIMIT 30
_DISPLAY
LOOP UNTIL _KEYHIT