I volunteer in emergency shelters and a fair few pass through us. Most want to claim asylum, but they don't always know how, or are afraid to do it. We help them out with that. Many return to the street once they get refugee status - many rough sleepers are refugees. At that point we would help them into accommodation and employment.
Many are very highly educated, many are totally illiterate. In all the outrage of education being denied to girls in many countries, people tend to lose sight of the fact that it is often denied to boys as well, particularly of "desirable" demographics. Some are illiterate, but very skilled, for example, we have had several individuals who can't read or write, but are skilled surgeons! And have gone on to become health care workers and similar. We have also had some incredible craftsmen and women pass through our hands, and have gone on to successful careers.
Many many become teachers. Particularly maths teachers. There is a good chance many of your children are taught maths by a refugee, although you probably wouldn't know.
Of course a lot are open to exploitation, and end up in nail bars, car washes, building sites, bar work, and jumping at the offer of accommodation instead of wages, and that accommodation might literally be a six foot long stretch of dirty carpet in a shed or under someone's stairs.
I have taken in around 20 at different times. You can have hopes and dreams for them, but in the end they make their own decisions, based on their own expectations and standards for life.
Of course many of the young females get forced into prostitution, and sold as slaves. There is a thriving slave trade in london and across many other Northern European capitals , especially Amsterdam, where some men go to buy wives.
The children are often hidden. Parents are afraid to approach authorities for help in case their children are taken off them. I'm sorry to say I have seen this happen, so I understand the fear. This is why you see parents with young children begging on the street - they prefer to sleep rough together than risk never seeing their children again.