Needs advice for a friend who has overstayed

[Jackdawson]

Hi
I'm trying to find out if there is anyway my mate who has overstayed his visa for over 2 yrs can sort the mess he has got himself in.
He was on student visa and tried to renew it ,sent the application to home office but failed to pay the visa fee and sincethen his visa and passport which is with home office must be expired
Meanwhile he carried on working and paying taxes which I think he was very lucky doing as his status probably didnt allow him to be employed.
Anyway he explained that his passport must have expired now and obviously same with his visa ( both are probably still with home office ) and now he isn't working but is having a baby with his partner who is British ,she is pregnant and had to start claiming benefits as she can't work anymore .
So in brief he sent his application for renewal didnt pay fee to home office passport and visa must b expired which are still with home office as he moved and now after 2 yrs cause he is having a baby and is with his partner for over a yr wants to sort his immigration status .
Is there anyway this guy can sort his mess and get proper visa and a new passport while living here and taking care of his new born baby