can anyone explain why a housemate who has heard the public booing them is so desperate to stay in the house, like Helen for instance, They must realise they cannot win so why do they want to stay knowing how they are unpopular with the public.

Maybe they're scared of going out and think given more time they can turn it around and turn those boos into cheers?

Ash was cheered then booed and then cheered.
Ashleigh was booed and then massively cheered.
A silly thread.

They also hear people booed then cheered and vice versa. Noone knows whether they will win or not tight up to the end. Makosi came third and constantly got booed.

A lot of people who have been in the house in the past have said that when they were in there they felt secure and didnt want to come out....

I agree.
Plus the crowd outside doesn't represent everyone, take Aron for instance, he was up 5 times if I remember correctly and booed every week. He ended up winning and was even booed leaving the house.