Hello,
Scholarships for LLM Programs exist?
If the candidate has a family, can his/her family follow? I mean - accommodation for family and ...
Thank you in advance for your answers.

Yes, scholarships exist. They can be either merit scholarships, which are awarded on academic work, quality work experience, etc.; there are also other scholarships for people of certain backgrounds, scholarships that are specifically for women. At the better schools scholarships can be hard to come by simply because they're more competitive and people are generally willing to pay more for a top degree.

For accompanying family, you should look into visa issues at the schools you're applying at. I know that in the US, you have to demonstrate that you're able to support your family financially in order to get visas for them, for example. Different countries might have different rules.