Tom, what are 'stub streets'? Haven't heard the term here.
The problem of whether pedestrian connections off the end of cul-de-sacs is an interesting one. In terms of encouraging walking, these connections are supposed to be good because they improve connectivity which means reduced walking times etc. However there seems to be disagreement within the Crime Prevention Through Environmental Design field as to whether closed cul-de-sacs are better than interconnected ones in terms of crime and safety - it seems that the important thing is how the pedestrian connections are designed. To maximise safety, they should be wide, well-lit, straight so they maintain sightlines, and should be able to be observed from neighbouring properties. Well that's what I've read anyway!
Some interesting findings from some Australian research on burglary risk in cul-de-sacs:
Being on "pure" cul-de-sacs decreases risk by about 28% (Axially straight, no pedestrian links)
Being on an "impure" cul-de-sac increases risk by about 22% (Axially complex, with pedestrian links)
Being "first in line" to a cul-de-sac decreases risk by about 25% (Increased movement, ie cars and people go past twice, in and out)