The answer could be rather simple:
Harry and Hagrid may not have had any wizarding next-of-kin. From Goblet of Fire
'Tha' was taken jus' after I got inter Hogwarts,' said Hagrid,
croakily. 'Dad was dead chuffed – thought I migh' not be a wizard,
see, 'cos me mum – well, anyway. 'Course, I never was great shakes at
magic, really – but at least he never saw me expelled. Died, see, in
me second year.
Hagrid's mother, of course, was the giantess Fridwulfa, and as such probably had very few rights under international magical law.
Harry's parents, of course, were dead. His guardians were Muggles, and to the best of my knowledge no other living relatives were ever mentioned.
It is possible that standard ministry policy is to give a wand to the closest wizard relative when someone is expelled or imprisoned. It is also possible that procedure is to snap a wand only when someone is expelled, rather than imprisoned. Rather like how, in the real world, an earned degree might be revoked for research misconduct, but probably not for murder or indeed war crimes (Saif al-Islam). Regardless, if the wand is not snapped it may well go to next-of-kin (if they are wizards, of course).
If Harry and Hagrid either lacked magical next-of-kin, or whatever kin they did have were simply too far-flung or distant, their wands might have become government property. And if the government decided that it had no use for them, they might have been destroyed.
Indeed, Bellatrix's wand probably went to Narcissa Malfoy, her richest and most "respectable" sister. One has no doubt that the Malfoys would have been willing to reunite Bellatrix with her wand.
Sirius probably did not have his own wand. He used a knife to try to kill Pettigrew, to start with.
For another, he used Snape's wand to transform Pettigrew.
Black had already retrieved Snape's wand from the bed. He approached
Lupin and the struggling rat, and his wet eyes suddenly seemed to be
burning in his face.
It seems almost certain that on the occasion he needed a wand thereafter (for example the battle at the Department of Mysteries), he borrowed one from an Order member--perhaps even a spare that they had inherited from a deceased relative.