How can one repent, restore rights to their owners, and get rid of ill-gotten money in the case of theft from work, while preserving one's dignity and not exposing oneself and one's family, especially when the stolen money is all that remains?

You have done well by repenting from sins, for Allah transforms evil deeds into good ones for the repentant.

It is not permissible to assist a thief, and you are responsible for the stolen money unless it is returned.

The stolen money must be returned to its owner, even through indirect means. Donating it as charity is not sufficient unless it is impossible to deliver it.

Conceal what happened and do not inform anyone about it, and return the right to its owner.

If not all the money is returned, you are responsible for the remainder, and it remains a debt upon you if you cannot find the owner.