How do the Azkaban escapees get their wands back?

The difference between a prison holding belongings for a prisoner when they are released and having the prisoner escape is that the escapee does so in secret and cannot gain their possessions back. For the escapees in the fifth book, we can assume their belongings were turned back over to them because the dementors had aligned with Voledmort- so while it was reported by the paper/ministry to be an escape, it was not the same kind of escape as say, Sirius or Croutch Jr. For Sirius, a true escapee of Azkaban, however this question is still a mystery.

My theory is that for Sirius, Dumbledore helped him get back and repair his wand, as the Elder Wand was the only thing powerful enough to repair a wand. Wands are buried with their masters, so it's doubtful that Sirius would have a family members, and he probably wouldn't want to even if he had the option.

In book 5, the first letter Harry receives after the Dementor attack clearly states that because of "the severity of this breach of the Decree for the Reasonable Regulation of Underage Sorcery has resulted in your expulsion from Hogwarts...and wand to be destroyed". So how can it be justified that Bellatrix who was convicted and sentenced for torture, did not have her wand destroyed, especially considering her wand was used in committing the crime. My guess is that your status, both blood and financial, play a role in what happens to your wand.

As for Voldemort's wand, presumably, Wormtail returns it to him when he finds him in Albania. Since Wormtail was the Potters' secret keeper, he would have been able fetch the wand after Voldemort tried to kill Harry.

But in Snape's memory, Snape is the first to arrive to the Potter house to see Lily's body and baby Harry is still in the crib, crying, which means Hagrid hadn't gotten there yet, since he fetched Harry under Dumbledore's orders, and didn't spot the wand. With all the rubble and chaos, maybe he wasn't worried about a wand, but doesn't that seem like the kind of detail Dumbledore would not have overlooked.

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.

It's likely that Dumbledore facilitated getting Sirius a new wand. Probably from Ollivander. Made precisely to the old wand's measurements or something.

What I want to know is... why does Ron use Charlie's old wand in the first two books. What's Charlie using?