All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
Your questions could be summarized as follows:
1) What is the ruling on the judge who concluded the marriage of your sister without contacting her family? Is he right in doing so? Is this marriage valid?
2) What is the ruling on your sister stealing the money on the grounds that it is her share in inheritance?
Before answering your questions, first we would like to mention that your sister running away for a distance of 800kms is wrong if no Mahram (non-Marriageable relative) accompanied her. The Prophet said: "It is not permissible for a woman who believes in Allaah and the Last Day to travel for a distance of one day and one night without a Mahram." [Al-Bukhari and Muslim]
As regards your first question, marriage without a guardian is not valid, this is the view of the majority of the scholars, and this is the correct opinion as the Prophet said: "Marriage without a guardian is invalid." [Ahmad] In this regard please refer to Fatwa 86773.
However, it is not permissible for a guardian to object to the marriage of a woman who is under his guardianship when a competent man whose religion and moral character are pleasing proposes to marry her. So if the guardian prevents her from marriage [without a sound religious reason] it is permissible for her to take the matter to a Muslim judge to marry her off or order one of her remote guardians to do so.
Therefore, if your sister was not wrongly prevented from marriage, then she was indeed wrong in concluding the marriage without the consent of her guardian.
Nonetheless, since the marriage contract was already concluded and it is no longer possible to do anything about it, then in our view, you should take the opinion of Imaam Abu Haneefah who is of the view that a guardian is not a pillar in marriage. This view is supported by the opinion of Imaam Maalik who considers that the marriage contract is correct if the woman is not forced to it and if an ordinary Muslim man is appointed as her guardian provided she is base or she is honourable but her husband had consummated the marriage with her since a long time. As regards the judge, he is not to be blamed if it was confirmed to him that her family are refusing to marry her off to a competent religious man, or that they live too far and it is not possible to contact them.
It should be noted that if your sister has children with this man, they will be traced back to him in any case, because the view that marriage without a guardian is valid, even it is not the most preponderant opinion; it is still considered a doubtful marriage which prevents the corporal punishment being applied, and the children from such marriage are traced back to the husband.
With regard to your second question, which is the money that your sister had taken when she ran away, if what she claimed is correct that it is her share of inheritance from your deceased father, in this case she is not considered sinful for taking the money; however, it was better if she had not taken it in such a manner. If she had no right in taking the money, then she is wrong by doing so but she is not considered as a thief who deserves corporal punishment unless if she had taken it secretly in a situation where there is no doubt that it is stealing. Thus, she is required to give it back to you [the heirs] unless you forgive her. The Prophet said: "A person who has taken anything is obliged to give it back [otherwise it will be a burden on his shoulders until he gives it back]."
Allaah Knows best.