Jobs provide the lowest common denominator social support system, which does not require extensive registration or a philosophy of charity or citizen status or a cousin on friendly terms or anything.
If there are jobs available, formal or informal, people will move.
There are no jobs available in the places they've been flooding into. They saturated the labor market. So they're trying to keep moving. Jobs are necessary to provide themselves with comfortable lives, rather than handouts that are limited in size and which could be snatched back at any point.
"I've heard there are jobs in California" during the Dust Bowl is a sentiment that would have made vast refugee camps if California had a moat around it and refused use of the bridges. Those people were not social parasites, they were fleeing exogenous conditions (war, drought) that destroyed their lifestyles, and they were seeking new ones.
Solitary asylum cases are a drastically different thing than mass movements of refugees claiming asylum. There is always an economic dimension to the latter; They have witnessed their whole society fall apart and spent or abandoned everything to escape, of course they're looking for jobs.
"Why do the “migrants” in Calais want to come to the UK?
This being the real world, there is no easy answer to the question “why?” Work, friends, family, language, historical links to the UK and, ironically, the UK’s reputation for fairness, tolerance and welcome all play their role."
https://www.freemovement.org.uk/why-do-the-migrants-in-calai...