Yes! I know of a guy who left the US 8 yrs ago as a GC holder and returned to India with the intention of giving up his GC. His siblings were against it and told him to return to India after taking the US citizenship. That didn't happen.
This guy got married and settled in India. He wanted to come for a visit to the US and so, he applied for a tourist visa last year. His application was denied by the US consulate. He then tried for a Canadian tourist visa and he was again denied.
The consulate asked him as to why he wanted to visit the US after giving up his GC. When he said that he wanted to see his family, he was told that his family can come to India to see him.
If a person gives up their GC, I guess the US consulates ask as to why such people would like to visit the US when they give up the GC voluntarily.