Say I have a Snit:
class Snit(): pass
And a Snot, which contains weak references to up to, say,          
        
Nothing is truly automatic.  You'll need to either have a function that you run manually to check for dead Snits, or have a function that is part of Snot that is called whenever anything interesting happens to a Snot to check for, and remove, dead Snits.
For example:
class Snot:
    ...
    def __repr__(self):
        # check for and remove any dead Snits
        self._remove_dead_snits()
        return ...
    def _remove_dead_snits(self):
        if self.s1() is None:
             self.s1 = None
        ... # and so on and so forth
The fun part is adding that call to _remove_dead_snits for every interesting interaction with a Snot -- such as __getitem__, __iter__, and whatever else you may do with it.
Actually, thinking a bit more about this, if you only have the four possible Snits per each Snot you could use a SnitRef descriptor -- here's the code, with some changes to your original:
import weakref
class Snit(object):
    def __init__(self, value):
        self.value = value  # just for testing
    def __repr__(self):
        return 'Snit(%r)' % self.value
class SnitRef(object):   # 'object' not needed in Python 3
    def __get__(self, inst, cls=None):
        if inst is None:
            return self
        return self.ref()  # either None or the obj
    def __set__(self, inst, obj):
        self.ref = weakref.ref(obj)
class Snot(object):
    s0 = SnitRef()
    s1 = SnitRef()
    s2 = SnitRef()
    s3 = SnitRef()
    def __init__(self,s0=None,s1=None,s2=None,s3=None):
        self.s0 = s0
        self.s1 = s1
        self.s2 = s2
        self.s3 = s3
snits = [Snit(0), Snit(1), Snit(2), Snit(3)]
print snits
snot = Snot(*snits)
print(snot.s2)
snits.pop(2)
print snits
print(snot.s2)
and when run:
[Snit(0), Snit(1), Snit(2), Snit(3)]
Snit(2)
[Snit(0), Snit(1), Snit(3)]
None