Welfarite provides some wise advice above. While this man thinks he is benefitting by working on the black economy and claiming his payment, in reality, the part-time work just boosts his social welfare payment and allow him to keep the lifestyle he has.
Working part-time work shows he capable of working for a wage, but it's unlikely he's getting any new skills that could help him secure full-time employment and move off social welfare.
In addition, having been unemployed for 2 years, his confidence in applying for work has probably been affected, so thinking about changing his situation is probably too overwhelming.
I agree that he should have a word with the Jobs Facilitator in his local social welfare office. Their role is to encourage clients to return to employment. They can look at his skills and put him in touch with other training and education providers who can assist with upskilling, etc. He may also find that he can retain his social welfare payment/benefits while he is undergoing training.
It's all very well of course talking about supports, training, payments and social welfare if the bottom line is this person doesn't want to return to employment or take the first steps themselves. At 28 years of age, there really is no reason why this man should not be in work, unless of course, there are other underlying issues.
You mentioned he suffered from serious depression last year; it is possible that this may still be affecting him and if so, shouldn't be underestimated. Depression following bereavement is very common and there are
a range of bereavement counselling services available nationally who may be able to help. (Or, his GP may be able to advise on a counselling service in his area). It might also be worth contacting
AWARE who provide support services for those affected by depression in his area.
This is a horrible situation for you to be in but hopefully the advice you have received here on AAM will help achieve a happy outcome for both of you.