Leaving and Entering on a Green Card - Criminal Record

Hi,

I have a family member which would really like to visit me in the UK. They are a citizen of a South American country and have a Green Card, and have lived in the USA for around 30 years. They fear leaving the USA as they have a Criminal Record. They were sentenced in 1984 for 6 years and were released in 1990. They have become very weary of this as they left and re-entered the USA in 1994 and were almost deported due to their record. They are very scared as they expect the same thing may happen again when they try to re-enter the USA on their Green Card.

They have tried to apply for US citizenship however, upon completion and pass on the US citizenship test, the application was declined on the basis of their criminal record.

Considering it has been 27 years since their release and 33 years since they were sentenced do you expect that this will cause them problems leaving and re-entering the USA.

I don't fully understand how they were allowed to still reside in the USA as a Green Card holder back in 1990 after their release because I would have expected them to have been deported. Am I right in thinking this? If anyone has any ideas how they still have managed to live in the USA lawfully for 33 years after being sentenced.

I understand a lawyer would be the first recommendation for this case and we do have a lawyer but they seem to be pretty unhopeful and any work that they have been doing for us has been taking a long period of time and no real explanations have been laid out.

Any ideas, suggestions, advice would be much appreciated.

Can someone please advise.