From language/operators

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The notandthen operator returns Empty upon encountering the first undefined argument, otherwise the last argument. Last argument is returned as-is, without being checked for definedness at all. Short-circuits. The result of the left side is bound to $_ for the right side, or passed as arguments if the right side is a Callable, whose .count must be 0 or 1.

At first glance, notandthen might appear to be the same thing as the orelse operator. The difference is subtle: notandthen returns Empty when it encounters a undefined item (that isn't the last item), whereas orelse returns that item. In other words, notandthen is a means to act when items aren't defined, whereas orelse is a means to obtain the first defined item:

sub all-sensors-down     { [notandthen] |@_, True             }
sub first-working-sensor { [orelse]     |@_, 'default sensor' }
 
all-sensors-down Nil, Nil, Nil
  and say 'OMG! All sensors are down!'; # OUTPUT:«OMG! All sensors are down!␤» 
say first-working-sensor Nil, Nil, Nil; # OUTPUT:«default sensor␤» 
 
all-sensors-down Nil, 42, Nil
  and say 'OMG! All sensors are down!'; # No output 
say first-working-sensor Nil, 42, Nil;  # OUTPUT:«42␤» 

The notandthen operator is a close relative of with statement modifier, and some compilers compile without to notandthen, meaning these two lines have equivalent behavior:

sub good-things { fail }
 
'boo'.say without good-things;
good-things() notandthen 'boo'.say;